results for au:Milburn_G in:quant-ph

- Dec 01 2017 cond-mat.mes-hall quant-ph arXiv:1711.11227v1We theoretically study the conditional counting statistics of electron transport through a system consisting of a single quantum dot (SQD) or coherently coupled double quantum dots (DQD's) monitored by a nearby quantum point contact (QPC) using the generating functional approach with the maximum eigenvalue of the evolution equation matrix method, the quantum trajectory theory method (Monte Carlo method), and an efficient method we develop. The conditional current cumulants that are significantly different from their unconditional counterparts can provide additional information and insight into the electron transport properties of mesoscopic nanostructure systems. The efficient method we develop for calculating the conditional counting statistics is numerically stable, and is capable of calculating the conditional counting statistics for a more complex system than the maximum eigenvalue method and for a wider range of parameters than the quantum trajectory method. We apply our method to investigate how the QPC shot noise affects the conditional counting statistics of the SQD system, going beyond the treatment and parameter regime studied in the literature. We also investigate the case when the interdot coherent coupling is comparable to the dephasing rate caused by the back action of the QPC in the DQD system, in which there is considerable discrepancy in the calculated conditional current cumulants between the population rate (master-) equation approach of sequential tunneling and the full quantum master-equation approach of coherent tunneling.
- Oct 27 2017 quant-ph arXiv:1710.09523v1In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.
- Aug 09 2017 quant-ph arXiv:1708.02369v1We introduce a quantum thermodynamic system that can operate as a thermal clock in analogy with the thermal clock first introduced by Ernst Mach in which the temperature difference between cooling bodies in contact can be used as a kind of relational time. Our model is based on an optomechanical system in which photons are transferred irreversibly between two cavities due to the modulation of the cavity cooling rate by a mechanical system coupled to a heat bath. We contrast the ensemble average view with a single system view using the theory of continuous measurement and we show that, by making a weak continuous measurement of the energy difference between the systems, a natural Mach thermal clock arises in an appropriate semiclassical limit. We investigate how quantum fluctuations modify this result.
- Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.
- Jul 12 2017 physics.hist-ph quant-ph arXiv:1707.03286v1Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research.
- May 12 2017 quant-ph arXiv:1705.04130v1In a seminal paper (Page and Wootters 1983) Page and Wootters suggest time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the "problem of time" stemming from vanishing Hamiltonian dynamics in many theories of quantum gravity. Their approach to relational time centres around the existence of a Hamiltonian and the subsequent constraint on physical states. In this paper we present a "state-centric" reformulation of the Page and Wootters model better suited to theories which intrinsically lack Hamiltonian dynamics, such as Chern--Simons theories. We describe relational time by encoding logical "clock" qubits into anyons---the topologically protected degrees of freedom in Chern--Simons theories. The timing resolution of such anyonic clocks is determined by the universality of the anyonic braid group, with non-universal models naturally exhibiting discrete time. We exemplify this approach using SU(2)$_2$ anyons and discuss generalizations to other states and models.
- Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum properties, such as entanglement, may exhibit entirely different behavior to purely classical systems. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph and coworkers [T C Ralph, G J Milburn, and T Downes, Phys. Rev. A, 79(2):22121, 2009, T C Ralph and J Pienaar, New Journal of Physics, 16(8):85008, 2014], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's (ESA) Space QUEST (Space - Quantum Entanglement Space Test) mission, and study the feasibility of the mission schema.
- Mar 17 2017 quant-ph cond-mat.quant-gas arXiv:1703.05666v2We propose a scheme to generate macroscopic superposition states in spin ensembles, where a coherent driving field is applied to accelerate the generation of macroscopic superposition states. The numerical calculation demonstrates that this approach allows us to generate a superposition of two classically distinct states of the spin ensemble with a high fidelity above 0.96 for 300 spins. For the larger spin ensemble, though the fidelity slightly decline, it maintains above 0.85 for an ensemble of 500 spins. The time to generate a macroscopic superposition state is also numerically calculated, which shows that the significantly shortened generation time allows us to achieve such macroscopic superposition states within a typical coherence time of the system.
- Among the many controversial aspects of the quantum / classical boundary, the emergence of chaos remains amongst the least experimentally verified. In particular, the time-resolved observation of quantum chaotic dynamics, and its interplay with quantum measurement, is largely unexplored outside experiments in atomic ensembles. We present here a realistic proposal to construct a chaotic driven top from the nuclear spin of a single donor atom in silicon, in the presence of nuclear quadrupole interaction. This system is exquisitely measurable and controllable, and possesses extremely long intrinsic quantum coherence times, allowing for the observation of subtle dynamical behavior over extended periods. We show that signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling.
- Feb 08 2017 quant-ph arXiv:1702.01845v1Despite the tremendous empirical success of quantum theory there is still widespread disagreement about what it can tell us about the nature of the world. A central question is whether the theory is about our knowledge of reality, or a direct statement about reality itself. Regardless of their stance on this question, current interpretations of quantum theory regard the Born rule as fundamental and add an independent state-update (or "collapse") rule to describe how quantum states change upon measurement. In this paper we present an alternative perspective and derive a probability rule that subsumes both the Born rule and the collapse rule. We show that this more fundamental probability rule can provide a rigorous foundation for informational, or "knowledge-based", interpretations of quantum theory.
- We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to detection of gravitational waves using the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.
- In this work we consider a recent proposal in which gravitational interactions are mediated via classical information and apply it to a relativistic context. We study a toy model of a quantized Friedman-Robertson-Walker (FRW) universe with the assumption that any test particles must feel a classical metric. We show that such a model results in decoherence in the FRW state that manifests itself as a dark energy fluid that fills the spacetime. Analysis of the resulting fluid, shows the equation of state asymptotically oscillates around the value $w=-1/3$, regardless of the spatial curvature, which provides the bound between accelerating and decelerating expanding FRW cosmologies. Motivated by quantum-classical interactions this model is yet another example of theories with violation of energy-momentum conservation whose signature could have significant consequences for the observable universe.
- Apr 08 2016 quant-ph cond-mat.mes-hall arXiv:1604.01834v1We propose and analyse a quantum electromechanical system composed of a monolithic quartz bulk acoustic wave (BAW) oscillator coupled to a superconducting transmon qubit via an intermediate LC electrical circuit. Monolithic quartz oscillators offer unprecedentedly high effective masses and quality factors for the investigation of mechanical oscillators in the quantum regime. Ground-state cooling of such mechanical modes via resonant piezoelectric coupling to an LC circuit, which is itself sideband cooled via coupling to a transmon qubit, is shown to be feasible. The fluorescence spectrum of the qubit, containing motional sideband contributions due to the couplings to the oscillator modes, is obtained and the imprint of the electromechanical steady-state on the spectrum is determined. This allows the qubit to function both as a cooling resource for, and transducer of, the mechanical oscillator. The results described are relevant to any hybrid quantum system composed of a qubit coupled to two (coupled or uncoupled) thermal oscillator modes.
- Mar 30 2016 quant-ph arXiv:1603.08613v2Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Preparing the mechanical resonator in non-classical states enables an optomechanical Stern-Gerlach interferometer. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, we recover single photon and two-photon interference via a classically controlled beam splitter. The visibility of the two-photon interference is particularly sensitive to coherent excitations in the mechanical resonator and this could form the basis of an optically transduced weak-force sensor.
- Oct 23 2015 quant-ph arXiv:1510.06483v1In this work we theoretically investigate a hybrid system of two optomechanically coupled resonators, which exhibits induced transparency. This is realized by coupling an optical ring resonator to a toroid. In the semiclassical analyses, the system displays bistabilities, isolated branches (isolas) and self-sustained oscillation dynamics. Furthermore, we find that the induced transparency transparency window sensitively relies on the mechanical motion. Based on this fact, we show that the described system can be used as a weak force detector and the optimal sensitivity can beat the standard quantum limit without using feedback control or squeezing under available experimental conditions.
- Aug 10 2015 quant-ph cond-mat.mes-hall arXiv:1508.01662v1Measuring thermodynamic quantities can be easy or not, depending on the system that is being studied. For a macroscopic object, measuring temperatures can be as simple as measuring how much a column of mercury rises when in contact with the object. At the small scale of quantum electromechanical systems, such simple methods are not available and invariably detection processes disturb the system state. Here we propose a method for measuring the temperature on a suspended semiconductor membrane clamped at both ends. In this method, the membrane is mediating a capacitive coupling between two transmission line resonators (TLR). The first TLR has a strong dispersion, that is, its decaying rate is larger than its drive, and its role is to pump in a pulsed way the interaction between the membrane and the second TLR. By averaging the pulsed measurements of the quadrature of the second TLR we show how the temperature of the membrane can be determined. Moreover the statistical description of the state of the membrane, which is directly accessed in this approach is significantly improved by the addition of a Josephson Junction coupled to the second TLR.
- Mar 10 2015 quant-ph arXiv:1503.02640v1Do the laws of quantum physics still hold for macroscopic objects - this is at the heart of Schrödinger's cat paradox - or do gravitation or yet unknown effects set a limit for massive particles? What is the fundamental relation between quantum physics and gravity? Ground-based experiments addressing these questions may soon face limitations due to limited free-fall times and the quality of vacuum and microgravity. The proposed mission MAQRO may overcome these limitations and allow addressing those fundamental questions. MAQRO harnesses recent developments in quantum optomechanics, high-mass matter-wave interferometry as well as state-of-the-art space technology to push macroscopic quantum experiments towards their ultimate performance limits and to open new horizons for applying quantum technology in space. The main scientific goal of MAQRO is to probe the vastly unexplored "quantum-classical" transition for increasingly massive objects, testing the predictions of quantum theory for truly macroscopic objects in a size and mass regime unachievable in ground-based experiments. The hardware for the mission will largely be based on available space technology. Here, we present the MAQRO proposal submitted in response to the (M4) Cosmic Vision call of the European Space Agency for a medium-size mission opportunity with a possible launch in 2025.
- Quantum mechanics and the theory of gravity are presently not compatible. A particular question is whether gravity causes decoherence - an unavoidable source of noise. Several models for gravitational decoherence have been proposed, not all of which can be described quantum mechanically. In parallel, several experiments have been proposed to test some of these models, where the data obtained by such experiments is analyzed assuming quantum mechanics. Since we may need to modify quantum mechanics to account for gravity, however, one may question the validity of using quantum mechanics as a calculational tool to draw conclusions from experiments concerning gravity. Here we propose an experiment to estimate gravitational decoherence whose conclusions hold even if quantum mechanics would need to be modified. We first establish a general information-theoretic notion of decoherence which reduces to the standard measure within quantum mechanics. Second, drawing on ideas from quantum information, we propose a very general experiment that allows us to obtain a quantitative estimate of decoherence of any physical process for any physical theory satisfying only very mild conditions.Finally, we propose a concrete experiment using optomechanics to estimate gravitational decoherence in any such theory, including quantum mechanics as a special case. Our work raises the interesting question whether other properties of nature could similarly be established from experimental observations alone - that is, without already having a rather well formed theory of nature like quantum mechanics to make sense of experimental data.
- Feb 13 2015 quant-ph physics.optics arXiv:1502.03553v2Photonic-crystal-based integrated optical systems have been used for a broad range of sensing applications with great success. This has been motivated by several advantages such as high sensitivity, miniaturization, remote sensing, selectivity and stability. Many photonic crystal sensors have been proposed with various fabrication designs that result in improved optical properties. In parallel, integrated optical systems are being pursued as a platform for photonic quantum information processing using linear optics and Fock states. Here we propose a novel integrated Fock state optical sensor architecture that can be used for force, refractive index and possibly local temperature detection. In this scheme, two coupled cavities behave as an "effective beam splitter". The sensor works based on fourth order interference (the Hong-Ou-Mandel effect) and requires a sequence of single photon pulses and consequently has low pulse power. Changes in the parameter to be measured induce variations in the effective beam splitter reflectivity and result in changes to the visibility of interference. We demonstrate this generic scheme in coupled L3 photonic crystal cavities as an example and find that this system, which only relies on photon coincidence detection and does not need any spectral resolution, can estimate forces as small as $10^{-7}$ Newtons and can measure one part per million change in refractive index using a very low input power of $10^{-10}$W. Thus linear optical quantum photonic architectures can achieve comparable sensor performance to semiclassical devices.
- Jan 29 2015 quant-ph arXiv:1501.07026v1For every N-qubit density matrix written in the computational basis, an associated "X-density matrix" can be obtained by vanishing all entries out of the main- and anti-diagonals. It is very simple to compute the genuine multipartite (GM) concurrence of this associated N-qubit X-state, which, moreover, lower bounds the GM-concurrence of the original (non-X) state. In this paper, we rely on these facts to introduce and benchmark a heuristic for estimating the GM-concurrence of an arbitrary multiqubit mixed state. By explicitly considering two classes of mixed states, we illustrate that our estimates are usually very close to the standard lower bound on the GM-concurrence, being significantly easier to compute. In addition, while evaluating the performance of our proposed heuristic, we provide the first characterization of GM-entanglement in the steady states of the driven Dicke model at zero temperature.
- Oct 20 2014 quant-ph arXiv:1410.4640v1We show that the two-axis counter twisting interaction squeezes a coherent spin state into three states of interest in quantum information, namely, the twin-Fock state, the equally-weighted superposition state, and the state that achieves the Heisenberg limit of optimal sensitivity defined by the Cramer-Rao inequality in addition to the well-known Heisenberg-limited state of spin fluctuations.
- May 23 2014 quant-ph arXiv:1405.5656v1Syndrome measurements made in quantum error correction contain more information than is typically used. We show that the statistics of data from syndrome measurements can be used to do the following: (i) estimation of parameters of an error channel, including the ability correct away the invertible part of the error channel, once it is estimated; (ii) hypothesis testing (or model selection) to distinguish error channels, e.g., to determine if the errors are correlated. The unifying theme is to make use of all of the information in the statistics of the data collected from syndrome measurements using machine learning and control algorithms.
- May 06 2014 quant-ph arXiv:1405.1010v1Detection of quantum features in mechanical systems at the nanoscale constitutes a challenging task, given the weak interaction with other elements and the available technics. Here we describe how the interaction between two monomodal transmission-line resonators (TLRs) mediated by vibrations of a nano-electromechanical oscillator can be described. This scheme is then employed for quantum non-demolition detection of the number of phonons in the nano-electromechanical oscillator through a direct current measurement in the output of one of the TLRs. For that to be possible an undepleted field inside one of the TLR works as a amplifier for the interaction between the mechanical resonator and the remaining TLR. We also show how how the non-classical nature of this system can be used for generation of tripartite entanglement and conditioned mechanical coherent superposition states, which may be further explored for detection processes.
- Apr 15 2014 quant-ph arXiv:1404.3214v2Newtonian gravity yields specific observable consequences, the most striking of which is the emergence of a $1/r^2$ force. In so far as communication can arise via such interactions between distant particles, we can ask what would be expected for a theory of gravity that only allows classical communication. Many heuristic suggestions for gravity-induced decoherence have this restriction implicitly or explicitly in their construction. Here we show that communication via a $1/r^2$ force has a minimum noise induced in the system when the communication cannot convey quantum information, in a continuous time analogue to Bell's inequalities. Our derived noise bounds provide tight constraints from current experimental results on any theory of gravity that does not allow quantum communication.
- Mar 19 2014 quant-ph arXiv:1403.4465v2Detecting an itinerant microwave photon with high efficiency is an outstanding problem in microwave photonics and its applications. We present a scheme to detect an itinerant microwave photon in a transmission line via the nonlinearity provided by a transmon in a driven microwave resonator. With a single transmon we achieve 84% distinguishability between zero and one microwave photons and 90% distinguishability with two cascaded transmons by performing continuous measurements on the output field of the resonator. We also show how the measurement diminishes coherence in the photon number basis thereby illustrating a fundamental principle of quantum measurement: the higher the measurement efficiency, the faster is the decoherence.
- We show that, by treating the gravitational interaction between two mechanical resonators as a classical measurement channel, a gravitational decoherence model results that is equivalent to a model first proposed by Diosi. The resulting decoherence model implies that the classically mediated gravitational interaction between two gravitationally coupled resonators cannot create entanglement. The gravitational decoherence rate ( and the complementary heating rate) is of the order of the gravitationally induced normal mode splitting of the two resonators.
- Nov 26 2013 quant-ph cond-mat.mes-hall arXiv:1311.6321v1Circuit cavity quantum electrodynamics (QED) is proving to be a powerful platform to implement quantum feedback control schemes due to the ability to control superconducting qubits and microwaves in a circuit. Here, we present a simple and promising quantum feedback control scheme for deterministic generation and stabilization of a three-qubit $W$ state in the superconducting circuit QED system. The control scheme is based on continuous joint Zeno measurements of multiple qubits in a dispersive regime, which enables us not only to infer the state of the qubits for further information processing but also to create and stabilize the target $W$ state through adaptive quantum feedback control. We simulate the dynamics of the proposed quantum feedback control scheme using the quantum trajectory approach with an effective stochastic maser equation obtained by a polaron-type transformation method and demonstrate that in the presence of moderate environmental decoherence, the average state fidelity higher than $0.9$ can be achieved and maintained for a considerable long time (much longer than the single-qubit decoherence time). This control scheme is also shown to be robust against measurement inefficiency and individual qubit decay rate differences. Finally, the comparison of the polaron-type transformation method to the commonly used adiabatic elimination method to eliminate the cavity mode is presented.
- Aug 17 2013 quant-ph arXiv:1308.3522v2We explore the effect of all-optical feedback on the steady state dynamics of optomechanical arrays arising from various topologies. First we consider an array comprised of a pair of independent optomechanical cavities coupled reversibly via their optical modes. Next we consider an optomechanical network formed from coupling two optical modes with interactions mediated via a common mechanical mode. Finally we extend the analysis to a large network of N-coupled optomechanical systems. Our results show implementing an-all optical feedback loop in each arrangement can enhance the degree of steady state entanglement between inter cavity optical and mechanical modes.
- Jun 07 2013 quant-ph arXiv:1306.1483v3Almost 60 years ago Dicke introduced the term superradiance to describe a signature quantum effect: N atoms can collectively emit light at a rate proportional to N^2. Even for moderate N this represents a significant increase over the prediction of classical physics, and the effect has found applications ranging from probing exciton delocalisation in biological systems, to developing a new class of laser, and even in astrophysics. Structures that super-radiate must also have enhanced absorption, but the former always dominates in natural systems. Here we show that modern quantum control techniques can overcome this restriction. Our theory establishes that superabsorption can be achieved and sustained in certain simple nanostructures, by trapping the system in a highly excited state while extracting energy into a non-radiative channel. The effect offers the prospect of a new class of quantum nanotechnology, capable of absorbing light many times faster than is currently possible; potential applications of this effect include light harvesting and photon detection. An array of quantum dots or a porphyrin ring could provide an implementation to demonstrate this effect.
- May 17 2013 quant-ph cond-mat.mes-hall arXiv:1305.3781v2We study single photon optomechanics conditioned on photon counting events. By selecting only detection events that occur long after a photon pulse arrives at the cavity, the optomechanical interaction time can be increased, allowing a large momentum kick to be applied to the oscillator. We apply this to two optomechanical cavities set up within a Mach-Zhender interferometer driven by a single photon source. The conditional state of the mechanical modes in such a system becomes an entangled cat state for detection times resulting in maximum mechanical amplitude in phase space. Further we study the dynamics induced by a second photon pulse injected into an already conditioned optomechanical cavity, a quarter of a mechanical period after the first photon has been detected. We illustrate how the optomechanical interaction resulting from the second photon can be strongly suppressed allowing conditional optomechanical routing of single photons with single photon control pulses.
- Multipartite entanglement of large numbers of physically distinct linear resonators is of both fundamental and applied interest, but there have been no feasible proposals to date for achieving it. At the same time, the Bose-Hubbard model with attractive interactions (ABH) is theoretically known to have a phase transition from the superfluid phase to a highly entangled nonlocal superposition, but observation of this phase transition has remained out of experimental reach. In this theoretical work, we jointly address these two problems by (1) proposing an experimentally accessible quantum simulation of the ABH phase transition in an array of tunably coupled superconducting circuit microwave resonators and (2) incorporating the simulation into a highly scalable protocol that takes as input any microwave resonator state with negligible occupation of number states |0> and |1> and nonlocally superposes it across the whole array of resonators. The large-scale multipartite entanglement produced by the protocol is of the W-type, which is well-known for its robustness. The protocol utilizes the ABH phase transition to generate the multipartite entanglement of all of the resonators in parallel, and is therefore deterministic and permits an increase in resonator number without increase in protocol complexity; the number of resonators is limited instead by system characteristics such as resonator frequency disorder and inter-resonator coupling strength. Only one local and two global controls are required for the protocol. We numerically demonstrate the protocol with realistic system parameters, and estimate that current experimental capabilities can realize the protocol with high fidelity for greater than 40 resonators.
- Dec 20 2012 quant-ph cond-mat.supr-con arXiv:1212.4795v2The iconic Schrödinger's cat state describes a system that may be in a superposition of two macroscopically distinct states, for example two clearly separated oscillator coherent states. Quite apart from their role in understanding the quantum classical boundary, such states have been suggested as offering a quantum advantage for quantum metrology, quantum communication and quantum computation. As is well known these applications have to face the difficulty that the irreversible interaction with an environment causes the superposition to rapidly evolve to a mixture of the component states in the case that the environment is not monitored. Here we show that by engineering the interaction with the environment there exists a large class of systems that can evolve irreversibly to a cat state. To be precise we show that it is possible to engineer an irreversible process so that the steady state is close to a pure Schrödinger's cat state by using double well systems and an environment comprising two-photon (or phonon) absorbers. We also show that it should be possible to prolong the lifetime of a Schrödinger's cat state exposed to the destructive effects of a conventional single-photon decohering environment. Our protocol should make it easier to prepare and maintain Schrödinger cat states which would be useful in applications of quantum metrology and information processing as well as being of interest to those probing the quantum to classical transition.
- Electromechanical systems currently offer a path to engineering quantum states of microwave and micromechanical modes that are of both fundamental and applied interest. Particularly desirable, but not yet observed, are mechanical states that exhibit entanglement, wherein non-classical correlations exist between distinct modes; squeezing, wherein the quantum uncertainty of an observable quantity is reduced below the standard quantum limit; and Schrödinger cats, wherein a single mode is cast in a quantum superposition of macroscopically distinct classical states. Also, while most investigations of electromechanical systems have focussed on single- or few-body scenarios, the many-body regime remains virtually unexplored. In such a regime quantum phase transitions naturally present themselves as a resource for quantum state generation, thereby providing a route toward entangling a large number of electromechanical systems in highly non-classical states. Here we show how to use existing superconducting circuit technology to implement a (quasi) quantum phase transition in an array of electromechanical systems such that entanglement, squeezing, and Schrödinger cats become simultaneously observable across multiple microwave and micromechanical oscillators.
- This book chapter reports on theoretical protocols for generating nonclassical states of light and mechanics. Nonclassical states are understood as squeezed states, entangled states or states with negative Wigner function, and the nonclassicality can refer either to light, to mechanics, or to both, light and mechanics. In all protocols nonclassicallity arises from a strong optomechanical coupling. Some protocols rely in addition on homodyne detection or photon counting of light.
- Oct 04 2012 quant-ph arXiv:1210.0991v1We show, in the context of single photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarisability model known as the cross-Kerr effect. We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single photon applications. Our results are presented in the context of a transmon in a one dimensional microwave waveguide, but the conclusions also apply to optical systems.
- Oct 03 2012 quant-ph arXiv:1210.0642v1We demonstrate that a geometric phase, generated via a sequence of four optomechanical interactions, can be used to increase, or generate nonlinearities in the unitary evolution of a mechanical resonator. Interactions of this form lead to new mechanisms for preparing mechanical squeezed states, and preparation of non-classical states with significant Wigner negativity.
- Photosynthetic light harvesting provides a natural blueprint for bioengineered and biomimetic solar energy and light detection technologies. Recent evidence suggests some individual light harvesting protein complexes (LHCs) and LHC subunits efficiently transfer excitons towards chemical reaction centers (RCs) via an interplay between excitonic quantum coherence, resonant protein vibrations, and thermal decoherence. The role of coherence in vivo is unclear however, where excitons are transferred through multi-LHC/RC aggregates over distances typically large compared with intra-LHC scales. Here we assess the possibility of long-range coherent transfer in a simple chromophore network with disordered site and transfer coupling energies. Through renormalization we find that, surprisingly, decoherence is diminished at larger scales, and long-range coherence is facilitated by chromophoric clustering. Conversely, static disorder in the site energies grows with length scale, forcing localization. Our results suggest sustained coherent exciton transfer may be possible over distances large compared with nearest-neighbour (n-n) chromophore separations, at physiological temperatures, in a clustered network with small static disorder. This may support findings suggesting long-range coherence in algal chloroplasts, and provides a framework for engineering large chromophore or quantum dot high-temperature exciton transfer networks.
- May 30 2012 quant-ph arXiv:1205.6461v1We propose a scheme for entangling the optical and microwave output modes of the respective cavities by using a micro mechanical resonator. The micro-mechanical resonator on one side is capacitively coupled to the microwave cavity and on the other side is coupled to a high finesses optical cavity. We then show how this continuous variable entanglement can be profitably used to teleport the non-Gaussian number state |1> and the superposition (|0>+|1>)/\surd2 from the microwave cavity output mode onto an output of optical cavity mode with fidelity much larger than the no-cloning limit.
- May 16 2012 quant-ph arXiv:1205.3240v2We describe a system composed of two coupled optical cavity modes with a coupling modulated by a bulk mechanical resonator. In addition, one of the cavity modes is irreversibly coupled to a single photon source. Our scheme is an opto-mechanical realisation of the Jaynes-Cummings model where the qubit is a dual rail optical qubit while the bosonic degree of freedom is a matter degree of freedom realised as the bulk mechanical excitation. We show the possibility of engineering phonon number states of the mechanical oscillator in such a system by computing the conditional state of the mechanics after successive photon counting measurements.
- Jan 25 2012 quant-ph arXiv:1201.5111v1We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalised in the basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalisation is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are similar in structure to recently proposed models for consistently combining quantum and classical stochastic dynamics.
- We show how to bridge the divide between atomic systems and electronic devices by engineering a coupling between the motion of a single ion and the quantized electric field of a resonant circuit. Our method can be used to couple the internal state of an ion to the quantized circuit with the same speed as the internal-state coupling between two ions. All the well-known quantum information protocols linking ion internal and motional states can be converted to protocols between circuit photons and ion internal states. Our results enable quantum interfaces between solid state qubits, atomic qubits, and light, and lay the groundwork for a direct quantum connection between electrical and atomic metrology standards.
- Oct 29 2011 quant-ph cond-mat.mes-hall arXiv:1110.6215v2We describe a reversible quantum interface between an optical and a microwave field using a hybrid device based on their common interaction with a micro-mechanical resonator in a superconducting circuit. We show that, by employing state-of-the-art opto-electro-mechanical devices, one can realise an effective source of (bright) two-mode squeezing with an optical idler (signal) and a microwave signal, which can be used for high-fidelity transfer of quantum states between optical and microwave fields by means of continuous variable teleportation.
- Sep 06 2011 quant-ph cond-mat.mes-hall arXiv:1109.0790v2We consider an array of three optomechanical cavities coupled either reversibly or irreversibly to each other and calculate the amount of entanglement between the different optical and mechanical modes. We show the composite system exhibits intercavity photon-phonon entanglement.
- Here we describe the quantum limit to measurement of the classical gravitational field. Specifically, we write down the optimal quantum Cramer-Rao lower bound, for any single parameter describing a metric for spacetime. The standard time-energy and Heisenberg uncertainty relations are shown to be special cases of the uncertainty relation for the spacetime metric. Four key examples are given, describing quantum limited estimation for: acceleration, black holes, gravitational waves and cosmology. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly spacetime independent derivation. The result is an uncertainty relation applicable to all causal spacetime manifolds.
- Jul 22 2011 quant-ph arXiv:1107.4152v3We propose a scheme able to generate stationary continuous variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a micro-mechanical resonator. We show that when both cavities are intensely driven one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and opto-mechanical entanglement.
- Jun 13 2011 quant-ph arXiv:1106.1992v1Single photons provide excellent quantum information carriers, but current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed single photons, while linear-optics gates are inherently probabilistic. Here, we introduce a deterministic scheme for photonic quantum information. Our single, versatile process---coherent photon conversion---provides a full suite of photonic quantum processing tools, from creating high-quality heralded single- and multiphoton states free of higher-order imperfections to implementing deterministic multiqubit entanglement gates and high-efficiency detection. It fulfils all requirements for a scalable photonic quantum computing architecture. Using photonic crystal fibres, we experimentally demonstrate a four-colour nonlinear process usable for coherent photon conversion and show that current technology provides a feasible path towards deterministic operation. Our scheme, based on interacting bosonic fields, is not restricted to optical systems, but could also be implemented in optomechanical, electromechanical and superconducting systems which exhibit extremely strong intrinsic nonlinearities.
- Using amplitude equations, we show that groups of identical nano-mechanical resonators, interacting with a common mode of a cavity microwave field, synchronize to form a single mechanical mode which couples to the cavity with a strength dependent on the square sum of the individual mechanical-microwave couplings. Classically this system is dominated by periodic behaviour which, when analyzed using amplitude equations, can be shown to exhibit multi-stability. In contrast groups of sufficiently dissimilar nano-mechanical oscillators may lose synchronization and oscillate out of phase at significantly higher amplitudes. Further the method by which synchronization is lost resembles that for large amplitude forcing which is not of the Kuramoto form.
- We describe an optomechanical system in which the mean phonon number of a single mechanical mode conditionally displaces the amplitude of the optical field. Using homodyne detection of the output field we establish the conditions under which phonon number quantum jumps can be inferred from the measurement record: both the cavity damping rate and the measurement rate of the phonon number must be much greater than the thermalization rate of the mechanical mode. We present simulations of the conditional dynamics of the measured system using the stochastic master equation. In the good-measurement limit, the conditional evolution of the mean phonon number shows quantum jumps as phonons enter and exit the mechanical resonator via the bath.
- Nov 04 2010 quant-ph cond-mat.mes-hall arXiv:1011.0879v2Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions.
- Nov 02 2010 cond-mat.quant-gas quant-ph arXiv:1011.0242v3The study of dynamical tunnelling in a periodically driven anharmonic potential probes the quantum-classical transition via the experimental control of the effective Planck's constant for the system. In this paper we consider the prospects for observing dynamical tunnelling with ultracold atoms in magnetic microtraps on atom chips. We outline the driven anharmonic potentials that are possible using standard magnetic traps, and find the Floquet spectrum for one of these as a function of the potential strength, modulation, and effective Planck's constant. We develop an integrable approximation to the non-integrable Hamiltonian and find that it can explain the behaviour of the tunnelling rate as a function of the effective Planck's constant in the regular region of parameter space. In the chaotic region we compare our results with the predictions of models that describe chaos-assisted tunnelling. Finally we examine the practicality of performing these experiments in the laboratory with Bose-Einstein condensates.
- We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.
- Sep 14 2010 quant-ph arXiv:1009.2306v2We investigate phase-insensitive linear amplification at the quantum limit for single- and two-mode states and show that there exists a broad class of non-Gaussian states whose nonclassicality survives even at an arbitrarily large gain. We identify the corresponding observable nonclassical effects and find that they include, remarkably, two-mode entanglement. The implications of our results for quantum cloning outside the Gaussian regime are also addressed.
- We propose a new experimental testbed that uses ions in the collective ground state of a static trap for studying the analog of quantum-field effects in cosmological spacetimes, including the Gibbons-Hawking effect for a single detector in de Sitter spacetime, as well as the possibility of modeling inflationary structure formation and the entanglement signature of de Sitter spacetime. To date, proposals for using trapped ions in analog gravity experiments have simulated the effect of gravity on the field modes by directly manipulating the ions' motion. In contrast, by associating laboratory time with conformal time in the simulated universe, we can encode the full effect of curvature in the modulation of the laser used to couple the ions' vibrational motion and electronic states. This model simplifies the experimental requirements for modeling the analog of an expanding universe using trapped ions and enlarges the validity of the ion-trap analogy to a wide range of interesting cases.
- Feb 23 2010 quant-ph cond-mat.mes-hall arXiv:1002.4055v2We propose a scheme for the quantum non-demolition (QND) measurement of Fock states of a nanomechanical resonator via feedback control of a coupled circuit QED system. A Cooper pair box (CPB) is coupled to both the nanoresonator and microwave cavity. The CPB is read-out via homodyne detection on the cavity and feedback control is used to effect a non-dissipative measurement of the CPB. This realizes an indirect QND measurement of the nanoresonator via a second-order coupling of the CPB to the nanoresonator number operator. The phonon number of the Fock state may be determined by integrating the stochastic master equation derived, or by processing of the measurement signal.
- Feb 09 2010 quant-ph arXiv:1002.1517v1We give a theoretical description of a coherently driven opto-mechanical system with a single added photon. The photon source is modeled as a cavity which initially contains one photon and which is irreversibly coupled to the opto-mechanical system. We show that the probability for the additional photon to be emitted by the opto-mechanical cavity will exhibit oscillations under a Lorentzian envelope, when the driven interaction with the mechanical resonator is strong enough. Our scheme provides a feasible route towards quantum state transfer between optical photons and micromechanical resonators.
- Dec 19 2009 quant-ph arXiv:0912.3547v1We study experimentally demonstrated single-electron ${}^{12}$C CNT QD with significant spin-orbit interaction as a scalable quantum computer candidate. Both electron spin and orbital angular momentum can serve as a logical qubit for quantum processing. We introduce macroscopic quantum memory for the system in a form of injected either magnetic or spin carrying atomic ensemble into the nanotube. CNT provides with a stable atomic trap in finite temperature and with one-dimensional nuclear spin lattice in an external magnetic field. The electron is coupled to the atomic ensemble through either magnetic or hyperfine interaction. Easy electron and nuclear spin read-out procedure for this system is possible.
- Oct 27 2009 quant-ph arXiv:0910.4772v1We investigate a doubly resonant optical cavity containing a Kerr nonlinear medium that couples two modes by a cross phase modulation. One of these modes is driven by a single photon pulsed field, and the other mode is driven by a coherent state. We find an intrinsic phase noise mechanism for the cross phase shift on the coherent beam which can be attributed to the random emission times of single photons from the cavity. An application to a weak nonlinearity phase gate is discussed.
- Sep 11 2009 quant-ph arXiv:0909.1846v3In this paper, we study the role of collective vibrational motion in the phenomenon of electronic energy transfer (EET) along a chain of coupled electronic dipoles with varying excitation frequencies. Previous experimental work on EET in conjugated polymer samples has suggested that the common structural framework of the macromolecule introduces correlations in the energy gap fluctuations which cause coherent EET. Inspired by these results, we present a simple model in which a driven nanomechanical resonator mode modulates the excitation energy of coupled quantum dots and find that this can indeed lead to an enhancement in the transport of excitations across the quantum network. Disorder of the on-site energies is a key requirement for this to occur. We also show that in this solid state system phase information is partially retained in the transfer process, as experimentally demonstrated in conjugated polymer samples. Consequently, this mechanism of vibration enhanced quantum transport might find applications in quantum information transfer of qubit states or entanglement.
- Jun 19 2009 quant-ph arXiv:0906.3317v1We describe an opto-mechanical system in which the coupling between optical and mechanical degrees of freedom takes the form of a fully quantised third-order parametric interaction. Two physical realisations are proposed: a harmonically trapped atom in a standing wave and the `membrane in the middle' model. The dominant resonant interaction corresponds to a stimulated Raman process in which two phonons are converted into a single cavity photon. We show that this system can exhibit a stable limit cycle in which energy is periodically exchanged between optical and mechanical degrees of freedom. This is equivalently described as a parametric self-pulsing.
- We consider the steady states of a harmonic oscillator coupled so strongly to a two-level system (a qubit) that the rotating wave approximation cannot be made. The Hamiltonian version of this model is known as the $E\otimes\beta$ Jahn-Teller model. The semiclassical version of this system exhibits a fixed point bifurcation, which in the quantum model leads to a ground state with substantial entanglement between the oscillator and the qubit. We show that the dynamical bifurcation survives in a dissipative quantum description of the system, amidst an even richer bifurcation structure. We propose two experimental implementations of this model based on superconducting cavities: a parametrically driven nonlinear nanomechanical resonator coupled capacitively to a coplanar microwave cavity and a superconducting junction in the central conductor of a coplanar waveguide.
- Feb 04 2009 quant-ph arXiv:0902.0402v2The very small size of optical nonlinearities places wide ranging restrictions on the types of novel physics one can explore. For an ensemble of multi-level systems one can synthesize a large effective optical nonlinearity using quantum coherence effects but such non-linearities are technically extremely challenging to demonstrate at the single atom level. In this work we describe how a single artificial multi-level Cooper Pair Box molecule, interacting with a superconducting microwave coplanar waveguide resonator, when suitably driven, can generate extremely large optical nonlinearities at microwave frequencies, with no associated absorption. We describe how the giant self-Kerr effect can be detected by measuring the second-order correlation function and quadrature squeezing spectrum.
- Oct 16 2008 quant-ph arXiv:0810.2618v1According to the Gottesmann-Knill theorem the non-Gaussian states are necessary component for a nontrivial quantum computation. We show two efficient and deterministic methods of $\chi^{(3)}$ non-Gaussian state generation for a cavity mode using a single trapped ion. Both require ion motional state transfer to the cavity field. The methods are experimentally feasible. The first is based on the well-known protocol for an ion finite motional superposition state generation. It allows for an arbitrary good approximation of $\chi^{(3)}$ non-Gaussian states. We give criteria based on the Wigner function which quantify the error resulting from the approximation. The second and novel method enables an exact non-Gaussian state generation using one laser pulse only.
- Sep 12 2008 quant-ph arXiv:0809.1907v1We discuss an alternative formulation of the problem of quantum optical fields in a curved space-time using localized operators. We contrast the new formulation with the standard approach and find observable differences for entangled states. We propose an experiment in which an entangled pair of optical pulses are propagated through non-uniform gravitational fields and find that the new formulation predicts de-correlation of the optical entanglement under experimentally realistic conditions.
- Aug 07 2008 quant-ph arXiv:0808.0743v3We propose the use of a superconducting charge qubit capacitively coupled to two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e. quantum superpositions of pairs of distinguishable coherent states 180$^\circ$ out of phase with each other. This is achieved by effectively implementing Kerr nonlinearities induced through application of a strong external driving field in one of the resonators. A simple study of the effect of dissipation on our scheme is also presented, and lower bounds of fidelity and purity of the generated state are calculated. Our procedure to implement a Kerr nonlinearity in this system may be used for high precision measurements in nanomechanical resonators.
- We investigate the noise properties of a superconducting single electron transistor (SSET) coupled to an harmonically driven resonator. Using a Langevin equation approach, we calculate the frequency spectrum of the SSET charge and calculate its effect on the resonator field. We find that the heights of the peaks in the frequency spectra depend sensitively on the amplitude of the resonator oscillation and hence suggest that the heights of these peaks could act as a sensitive signal for detecting the small changes in the amplitude of the drive. The previously known results for the effective amplitude-dependent damping and temperature provided by the SSET for the case of a low frequency resonator are generalized for all resonator frequencies.
- Jul 23 2008 quant-ph arXiv:0807.3500v1Spatial correlation functions provide a glimpse into the quantum correlations within a quantum system. Ions in a linear trap collectively form a nonuniform, discretized background on which a scalar field of phonons propagates. Trapped ions have the experimental advantage of each having their own "built-in" motional detector: electronic states that can be coupled, via an external laser, to the ion's vibrational motion. The post-interaction electronic state can be read out with high efficiency, giving a stochastic measurement record whose classical correlations reflect the quantum correlations of the ions' collective vibrational state. Here we calculate this general result, then we discuss the long detection-time limit and specialize to Gaussian states, and finally we compare the results for thermal versus squeezed states.
- Jun 06 2008 quant-ph arXiv:0806.0945v1The European Space Agency (ESA) has supported a range of studies in the field of quantum physics and quantum information science in space for several years, and consequently we have submitted the mission proposal Space-QUEST (Quantum Entanglement for Space Experiments) to the European Life and Physical Sciences in Space Program. We propose to perform space-to-ground quantum communication tests from the International Space Station (ISS). We present the proposed experiments in space as well as the design of a space based quantum communication payload.
- Apr 30 2008 quant-ph arXiv:0804.4540v1We consider a nanomechanical analogue of a nonlinear interferometer, consisting of two parallel, flexural nanomechanical resonators, each with an intrinsic Duffing nonlinearity and with a switchable beamsplitter-like coupling between them. We calculate the precision with which the strength of the nonlinearity can be estimated and show that it scales as $1/n^{3/2}$, where $n$ is the mean phonon number of the initial state. This result holds even in the presence of dissipation, but assumes the ability to make measurements of the quadrature components of the nanoresonators.
- Apr 24 2008 quant-ph arXiv:0804.3618v1We determine the small signal gain and noise response of an amplifier based on the nonlinear response of a quantum nanomechanical resonator. The resonator is biased in the nonlinear regime by a strong harmonic bias force and we determine the response to a small additional driving signal detuned with respect to the bias force.
- Mar 13 2008 quant-ph cond-mat.mes-hall arXiv:0803.1757v2We study a parametrically-driven nanomechanical resonator capacitively coupled to a microwave cavity. If the nanoresonator can be cooled to near its quantum ground state then quantum squeezing of a quadrature of the nanoresonator motion becomes feasible. We consider the adiabatic limit in which the cavity mode is slaved to the nanoresonator mode. By driving the cavity on its red-detuned sideband, the squeezing can be coupled into the microwave field at the cavity resonance. The red-detuned sideband drive is also compatible with the goal of ground state cooling. Squeezing of the output microwave field may be inferred using a technique similar to that used to infer squeezing of the field produced by a Josephson parametric amplifier, and subsequently, squeezing of the nanoresonator motion may be inferred. We have calculated the output field microwave squeezing spectra and related this to squeezing of the nanoresonator motion, both at zero and finite temperature. Driving the cavity on the blue-detuned sideband, and on both the blue and red sidebands, have also been considered within the same formalism.