results for au:Singh_V in:quant-ph

- We study the entanglement for a state on linked torus boundaries in $3d$ Chern-Simons theory with a generic gauge group and present the asymptotic bounds of Rényi entropy at two different limits: (i) large Chern-Simons coupling $k$, and (ii) large rank $r$ of the gauge group. These results show that the Rényi entropies cannot diverge faster than $\ln k$ and $\ln r$, respectively. We focus on torus links $T(2,2n)$ with topological linking number $n$. The Rényi entropy for these links shows a periodic structure in $n$ and vanishes whenever $n = 0 \text{ (mod } \textsf{p})$, where the integer $\textsf{p}$ is a function of coupling $k$ and rank $r$. We highlight that the refined Chern-Simons link invariants can remove such a periodic structure in $n$.
- Apr 21 2017 quant-ph cond-mat.mes-hall arXiv:1704.06208v1With the introduction of superconducting circuits into the field of quantum optics, many novel experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength $g$ can be increased until it is comparable with the atomic or mode frequency $\omega_{a,m}$ and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize the first Transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of $g/\omega_{m}=0.19$ and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size and localization of electric fields in vacuum, this new architecture offers the potential to further explore the novel regime of multi-mode ultra-strong coupling.
- Apr 17 2017 quant-ph cond-mat.mes-hall arXiv:1704.04421v1In this experiment, we couple a superconducting Transmon qubit to a high-impedance $645\ \Omega$ microwave resonator. Doing so leads to a large qubit-resonator coupling rate $g$, measured through a large vacuum Rabi splitting of $2g\simeq 910$ MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies $\omega$, placing our system close to the ultra-strong coupling regime ($\bar{g}=g/\omega=0.071$ on resonance). Combining this setup with a vacuum-gap Transmon architecture shows the potential of reaching deep into the ultra-strong coupling $\bar{g} \sim 0.45$ with Transmon qubits.
- Mar 07 2017 cond-mat.quant-gas quant-ph arXiv:1703.02024v1We investigate the superfluid behavior of a two-dimensional (2D) Bose gas of $^{87}$Rb atoms using classical field dynamics. In the experiment by R. Desbuquois \textitet al., Nat. Phys. \textbf8, 645 (2012), a 2D quasicondensate in a trap is stirred by a blue-detuned laser beam along a circular path around the trap center. Here, we study this experiment from a theoretical perspective. The heating induced by stirring increases rapidly above a velocity $v_c$, which we define as the critical velocity. We identify the superfluid, the crossover, and the thermal regime by a finite, a sharply decreasing, and a vanishing critical velocity, respectively. We demonstrate that the onset of heating occurs due to the creation of vortex-antivortex pairs. A direct comparison of our numerical results to the experimental ones shows good agreement, if a systematic shift of the critical phase-space density is included. We relate this shift to the absence of thermal equilibrium between the condensate and the thermal wings, which were used in the experiment to extract the temperature. We expand on this observation by studying the full relaxation dynamics between the condensate and the thermal cloud.
- Sep 09 2015 cond-mat.quant-gas quant-ph arXiv:1509.02168v2We investigate the superfluid behavior of a Bose-Einstein condensate of $^6$Li molecules. In the experiment by Weimer et al., Phys. Rev. Lett. 114, 095301 (2015) a condensate is stirred by a weak, red-detuned laser beam along a circular path around the trap center. The rate of induced heating increases steeply above a velocity $v_c$, which we define as the critical velocity. Below this velocity, the moving beam creates almost no heating. In this paper, we demonstrate a quantitative understanding of the critical velocity. Using both numerical and analytical methods, we identify the non-zero temperature, the circular motion of the stirrer, and the density profile of the cloud as key factors influencing the magnitude of $v_c$. A direct comparison to the experimental data shows excellent agreement.
- Aug 03 2015 cond-mat.mes-hall quant-ph arXiv:1507.08898v2In cavity optomechanics, light is used to control mechanical motion. A central goal of the field is achieving single-photon strong coupling, which would enable the creation of quantum superposition states of motion. Reaching this limit requires significant improvements in optomechanical coupling and cavity coherence. Here we introduce an optomechanical architecture consisting of a silicon nitride membrane coupled to a three-dimensional superconducting microwave cavity. Exploiting their large quality factors, we achieve an optomechanical cooperativity of 146,000 and perform sideband cooling of the kilohertz-frequency membrane motion to 34$\pm$5 $\mu$K, the lowest mechanical mode temperature reported to date. The achieved cooling is limited only by classical noise of the signal generator, and should extend deep into the ground state with superconducting filters. Our results suggest that this realization of optomechanics has the potential to reach the regimes of ultra-large cooperativity and single-photon strong coupling, opening up a new generation of experiments.
- We investigate theoretically in detail the non-linear effects in the response of an optical/microwave cavity coupled to a Duffing mechanical resonator. The cavity is driven by a laser at a red or blue mechanical subband, and a probe laser measures the reflection close to the cavity resonance. Under these conditions, we find that the cavity exhibits optomechanically induced reflection (OMIR) or absorption (OMIA) and investigate the optomechanical response in the limit of non-linear driving of the mechanics. Similar to linear mechanical drive, an overcoupled cavity the red-sideband drive may lead to both OMIA and OMIR depending on the strength of the drive, whereas the blue-sideband drive only leads to OMIR. The dynamics of the phase of the mechanical resonator leads to the difference between the shapes of the response of the cavity and the amplitude response of the driven Duffing oscillator, for example, at weak red-sideband drive the OMIA dip has no inflection point. We also verify that mechanical non-linearities beyond Duffing model have little effect on the size of the OMIA dip though they affect the width of the dip.
- In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparisons to classical systems. In this work, we explore the idea of extending Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with a dynamic selection function in contrast to the static selection function used in the original work (Grover in Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996). We show that this alteration facilitates us to extend the application of Grover search to the field of randomized search algorithms. Further, we use the dynamic Grover search algorithm to define the goals for a recommendation system based on which we propose a recommendation algorithm which uses binomial similarity distribution space giving us a quadratic speedup over traditional classical unstructured recommendation systems. Finally, we see how dynamic Grover search can be used to tackle a wide range of optimization problems where we improve complexity over existing optimization algorithms.
- Jan 15 2014 quant-ph arXiv:1401.3035v1We discuss two approaches to producing generalized parity proofs of the Kochen-Specker theorem. Such proofs use contexts of observables whose product is $I$ or $-I$; we call them constraints. In the first approach, one starts with a fixed set of constraints and methods of linear algebra are used to produce subsets that are generalized parity proofs. Coding theory methods are used for enumeration of the proofs by size. In the second approach, one starts with the combinatorial structure of the set of constraints and one looks for ways to suitably populate this structure with observables. As well, we are able to show that many combinatorial structures can not produce parity proofs.
- Apr 03 2012 quant-ph physics.atom-ph arXiv:1204.0352v2Single-photon cooling is a recently introduced method to cool atoms and molecules for which standard methods might not be applicable. We numerically examine this method in a two-dimensional wedge trap as well as in a two-dimensional harmonic trap. An element of the method is an optical dipole box trapping atoms irreversibly. We show that the cooling efficiency of the single-photon method can be improved by optimizing the trajectory of this optical dipole box.
- May 14 2008 physics.hist-ph quant-ph arXiv:0805.1780v1We recount the successful long career of classical physics, from Newton to Einstein, which was based on the philosophy of scientific realism. Special emphasis is given to the changing status and number of ontological entitities and arguments for their necessity at any time. Newton, initially, began with (i) point particles, (ii) aether, (iii) absolute space and (iv) absolute time. The electromagnetic theory of Maxwell and Faraday introduced `fields' as a new ontological entity not reducible to earlier ones. Their work also unified electricity, magnetism and optics. Repeated failure to observe the motion of earth through aether led Einstein to modify the Newtonian absolute space and time concepts to a fused Minkowski space-time and the removal of aether from basic ontological entities in his special theory of relativity. Later Einstein in his attempts to give a local theory of gravitation was led to further modify flat Minkowski space-time to the curved Riemannian space time. This reduced gravitational phenomenon to that of geometry of the space time. Space-time, matter and fields all became dynamical. We also abstract some general features of description of nature in classical physics and enquire whether these could be features of any scientific description?
- May 14 2008 quant-ph physics.hist-ph arXiv:0805.1779v1A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.
- Jul 28 2006 quant-ph arXiv:quant-ph/0607192v2An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states.
- Oct 25 2005 quant-ph arXiv:quant-ph/0510180v1We review here the main contributions of Einstein to the quantum theory. To put them in perspective we first give an account of Physics as it was before him. It is followed by a brief account of the problem of black body radiation which provided the context for Planck to introduce the idea of quantum. Einstein's revolutionary paper of 1905 on light-quantum hypothesis is then described as well as an application of this idea to the photoelectric effect. We next take up a discussion of Einstein's other contributions to old quantum theory. These include (i) his theory of specific heat of solids, which was the first application of quantum theory to matter, (ii) his discovery of wave-particle duality for light and (iii) Einstein's A and B coefficients relating to the probabilities of emission and absorption of light by atomic systems and his discovery of radiation stimulated emission of light which provides the basis for laser action. We then describe Einstein's contribution to quantum statistics viz Bose-Einstein Statistics and his prediction of Bose-Einstein condensation of a boson gas. Einstein played a pivotal role in the discovery of Quantum mechanics and this is briefly mentioned. After 1925 Einstein's contributed mainly to the foundations of Quantum Mechanics. We choose to discuss here (i) his Ensemble (or Statistical) Interpretation of Quantum Mechanics and (ii) the discovery of Einstein-Podolsky-Rosen (EPR) correlations and the EPR theorem on the conflict between Einstein-Locality and the completeness of the formalism of Quantum Mechanics. We end with some comments on later developments.
- Jul 20 2005 quant-ph arXiv:quant-ph/0507182v2We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and then analyse it's weakness in terms of Bell's explicit hidden variable model of spin one-half particles. We next discuss Gleason's theorem and Kochen-Specker theorem and bring out the troublems with non contextual hidden variable theories. An important role is played by Einstein locality in the discussion of hidden variable theories as was first brought out by Einstein, Podolsky and Rosen. We elaborate it's various implications such as Bell's theorem in terms of Bell's inequalities as well as later work in which Bell's theorem follows without using inequalities.
- Dec 21 2004 quant-ph arXiv:quant-ph/0412148v1We begin by discussing ``What exists?'', i.e. ontology, in Classical Physics which provided a description of physical phenomena at the macroscopic level. The microworld however necessitates a introduction of Quantum ideas for its understanding. It is almost certain that the world is quantum mechanical at both microscopic as well as at macroscopic level. The problem of ontology of a Quantum world is a difficult one. It also depends on which interpretation is used. We first discuss some interpretations in which Quantum Mechanics does not provide a complete framework but has to be supplemented by extra ingredients e.g. (i) Copenhagen group of interpretations associated with the names of Niels Bohr, Heisenberg, von-Neumann, and (ii) de-Broglie-Bohm interpretations. We then look at some interpretations in which Quantum mechanics is supposed to provide the entire framework such as (i) Everett-deWitt many world, (ii) quantum histories interpretations. We conclude with some remarks on the rigidity of the formalism of quantum mechanics, which is sharp contrast to it's ontological fluidity.
- Feb 18 2004 quant-ph arXiv:quant-ph/0402113v2We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e. depending on a (complete) commuting set of $N$ variables, are considered. A diagrammatic or graph theoretic formulation of the problem is developed. We then exactly determine the set of ``admissible'' data, i.e. those types of data for which the problem always admits solutions. This is done in the case where the joint distributions originate from quantum mechanics as well as in the case where this constraint is not imposed. In particular, it is shown that a necessary (but not sufficient) condition for the existence of solutions is $n\leq N+1$. When the data are admissible and the quantum constraint is not imposed, the general solution for the phase space density is determined explicitly. For admissible data of a quantum origin, the general solution is given in certain (but not all) cases. In the remaining cases, only a subset of solutions is obtained.
- May 30 2002 quant-ph arXiv:quant-ph/0205185v1We address the classical and quantum marginal problems, namely the question of simultaneous realizability through a common probability density in phase space of a given set of compatible probability distributions. We consider only distributions authorized by quantum mechanics, i.e. those corresponding to complete commuting sets of observables. For four-dimensional phase space with position variables qi and momentum variables pj, we establish the two following points: i) given four compatible probabilities for (q1,q2), (q1,p2), (p1,q2) and (p1,p2), there does not always exist a positive phase space density rho(qi,pj) reproducing them as marginals; this settles a long standing conjecture; it is achieved by first deriving Bell-like inequalities in phase space which have their own theoretical and experimental interest. ii) given instead at most three compatible probabilities, there always exist an associated phase space density rho(qi,pj); the solution is not unique and its general form is worked out. These two points constitute our ``three marginal theorem''.
- May 27 2002 quant-ph arXiv:quant-ph/0205157v1We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there exist quantum states for which more than three of the quantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and $(p_1,q_2)$ cannot be reproduced as marginals of a positive $\rho(\overrightarrow{q},\overrightarrow{p})$''. We also construct the most general positive $\rho(\overrightarrow{q},\overrightarrow{p})$ which reproduces any three of the above quantum probability densities for arbitrary quantum states. This is crucial for the construction of a maximally realistic quantum theory.
- We recently constructed a causal quantum mechanics in 2 dim. phase space which is more realistic than the de Broglie-Bohm mechanics as it reproduces not just the position but also the momentum probability density of ordinary quantum theory. Here we present an even more ambitious construction in 2n dim. phase space. We conjecture that the causal Hamiltonian quantum mechanics presented here is `maximally realistic'. The positive definite phase space density reproduces as marginals the correct quantum probability densities of $n+1$ different complete commuting sets of observables (e.g. $\vec q$, $\vec p$ and $n-1$ other sets). In general the particle velocities do not coincide with the de Broglie-Bohm velocities.