Uncovering a Nonclassicality of the Schr"odinger Coherent State up to the Macro-Domain (original) (raw)
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Nonclassicality of the Harmonic-Oscillator Coherent State Persisting up to the Macroscopic Domain
Physical Review Letters, 2018
Can the most "classical-like" of all quantum states, namely the Schrödinger coherent state of a harmonic oscillator, exhibit nonclassical behavior? We find that for an oscillating object initially in a coherent state, merely by observing at various instants which spatial region the object is in, the Leggett-Garg inequality (LGI) can be violated through a genuine negative result measurement, thereby repudiating the everyday notion of macrorealism. This violation thus reveals an unnoticed nonclassicality of the very state which epitomizes classicality within the quantum description. It is found that for any given mass and oscillator frequency, a significant quantum violation of LGI can be obtained by suitably choosing the initial peak momentum of the coherent state wave packet. It thus opens up potentially the simplest way (without coupling with any ancillary quantum system or using nonlinearity) for testing whether various recently engineered and sought after macroscopic oscillators, such as feedback cooled thermal trapped nanocrystals of ∼10 6-10 9 amu mass, are indeed bona fide nonclassical objects.
2020
We consider tests of Leggett-Garg’s macrorealism and of macroscopic local realism, where for spacelike separated measurements the assumption of macroscopic noninvasive measurability is justified by that of macroscopic locality. We give a mapping between the Bell and Leggett-Garg experiments for microscopic qubits based on spin 1/2 eigenstates and gedanken experiments for macroscopic qubits based on two macroscopically distinct coherent states (cat states). In this mapping, the unitary rotation of the Stern-Gerlach analyzer is realized by an interaction H = Ωn̂ where n̂ is the number of quanta. By adjusting the time of interaction, one alters the measurement setting. We thus predict violations of Leggett-Garg and Bell inequalities in a macroscopic regime where coarse-grained measurements M̂ need only discriminate between two macroscopically distinct coherent states. To interpret the violations, we distinguish between subtly different definitions of macroscopic realism. Deterministic ...
Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object
Physical Review X, 2015
While quantum mechanics exquisitely describes the behavior of microscopic systems, one ongoing challenge is to explore its applicability to systems of larger size and mass. Unfortunately, quantum states of increasingly macroscopic objects are more easily corrupted by unintentional measurements from the classical environment. Additionally, even the intentional measurements from the observer can further perturb the system 1 . In optomechanics 2 , coherent light fields serve as the intermediary between the fragile mechanical states and our inherently classical world by exerting radiation pressure forces and extracting mechanical information. Here we engineer a microwave cavity optomechanical system 3 to stabilize a nonclassical steady-state of motion while independently, continuously, and nondestructively monitoring it. By coupling the motion of an aluminum membrane to two microwave cavities, we separately prepare and measure a squeezed state of motion 4 . We demonstrate a quantum nondemolition (QND) measurement 5-7 of sub-vacuum mechanical quadrature fluctuations. The techniques developed here have direct applications 8 in the areas of quantum-enhanced sensing 9 and quantum information processing, and could be further extended to more complex quantum states 10 .
Quantum violation of classical physics in macroscopic systems
2016
While quantum theory has been tested to an incredible degree on microscopic scales, quantum effects are seldom observed in our everyday macroscopic world. The curious results of applying quantum mechanics to macroscopic objects are perhaps best illustrated by Erwin Schrödinger's famous thought experiment, where a cat can be put into a superposition state of being both dead and alive. Obviously, these quantum predictions are in stark contradiction to our common experience. Even with plenty of theoretical explanations put forward to explain this discrepancy, a large number of questions about the frontier between the quantum and the classical world remain unanswered. To distinguish between classical and quantum behavior, two fundamental concepts inherent to classical physics have been established over the years: The world view of local realism limits the power of classical experiments to establish correlations over space, while the world view of macroscopic realism (or macrorealism...
PRA
In 1985, Leggett and Garg formulated a class of inequalities for testing the compatibility between macroreal-ism and quantum mechanics. In this paper, we point out that, based on the same assumptions of macrorealism that are used to derive Leggett-Garg inequalities (LGIs), there is a scope of formulating another class of inequalities different from the standard LGIs. By considering the three-time measurement scenario in a dichotomic system, we first propose an interesting variant of the standard LGIs and show that its quantum violation is larger than the standard LGIs. By extending this formulation to the n-time measurement scenario, we found that the quantum violations of variants of the LGIs for a qubit system increase with n, and, for a sufficiently large n, an algebraic maximum can be reached. We then compare the violations of the standard and variants of the LGIs in an unsharp measurement scenario and show that, for any arbitrary n, the violation of the latter is more robust to unsharpness than the former. Furthermore, we examine the relation between the quantum violations of the variants of the LGIs and an another formulation macrorealism, known as no-signaling in time conditions.
Nonclassicality of states and measurements by breaking classical bounds on statistics
Physical Review A, 2009
We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are independent of other typical quantum signatures such as sub-Poissonian statistics, quadrature squeezing, or oscillatory statistics. This approach can be equally well applied to very diverse situations such as single-and two-mode fields, observables with continuous and discrete spectra, finite-and infinite-dimensional systems, and ideal and noisy measurements.
Reviews of Modern Physics, 1980
The monitoring of a quantum-mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. This paper reviews the standard techniques for monitoring the oscillator, and introduces a new technique which, in principle, cd determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator. The standard method for monitoring the oscillator is the "amplitude-andphase" method (position or momentum transducer with output fed through a narrow-band amplifier). The accuracy obtainable by this method is limited by the uncertainty principle ("standard quantum limit" ). To do better requires a measurement of the type which Braginsky has called "quantum nondemolition. " A well known quantum nondemolition technique is *'quantum counting, " which can detect an arbitrarily weak classical force, but which cannot provide good accuracy in determining its precise time dependence. This paper considers extensively a new type of quantum nondemolition measurementa "back-action-evading" measurement of the real part X, {or the imaginary part X2) of the oscillator's complex amplitude. In principle X, can be measured "arbitrarily quickly and arbitrarily accurately, " and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force. The authors describe explicit Gedanken experiments which demonstrate that X, can be measured arbitrarily quickly and arbitrarily accurately. In these experiments the measuring apparatus must be coupled to both the position {position transducer} and the momentum (momentum transducer) of the oscillator, and both couplings must be modulated sinusoidally. For a given measurement time the strength of the coupling determines the accuracy of the measurement; for arbitrarily strong coupling the measurement can be arbitrarily accurate. The momentum transducer" is constructed by combining a "velocity transducer" with a "negative capacitor'" or "negative spring. " The modulated couplings are provided by an external, -classical generator, which can be realized as a harmonic oscillator excited in an arbitrarily energetic, coherent state. One can avoid the use of two transducers by making "stroboscopic measurements" of X" in which one measures position (or momentum) at half-cycle intervals.
Experimental violation of Svetlichny's inequality
New Journal of Physics, 2009
It is well known that quantum mechanics is incompatible with local realistic theories. Svetlichny showed, through the development of a Bell-like inequality, that quantum mechanics is also incompatible with a restricted class of nonlocal realistic theories for three particles where any two-body nonlocal correlations are allowed . In the present work, we experimentally generate three-photon GHZ states to test Svetlichny's inequality. Our states are fully characterized by quantum state tomography using an overcomplete set of measurements and have a fidelity of (84±1)% with the target state. We measure a convincing, 3.6σ, violation of Svetlichny's inequality and rule out this class of restricted nonlocal realistic models. arXiv:0909.0789v1 [quant-ph]
Violation of classical inequalities by photon frequency filtering
Physical Review A, 2014
The violation of the Cauchy-Schwarz and Bell inequalities ranks among the major evidences of the genuinely quantum nature of an emitter. We show that by dispensing from the usual approximation of mode correlations and studying directly correlations between the physical reality-the photonsthese violations can be optimized. This is achieved by extending the concept of photon correlations to all frequencies in all the possible windows of detections, with no prejudice to the supposed origin of the photons. We identify the regions of quantum emission as rooted in collective de-excitation involving virtual states instead of, as previously assumed, cascaded transitions between real states. PACS numbers: 42.50.Ct, 42.50.Ar, 42.50.Pq Classical descriptions of the electromagnetic field [1] and local hidden variable theories [2] yield a series of inequalities that impose an upper limit to the correlations between two modes and whose violation prove unequivocally the non-classical character of quantum mechanics . Among such equalities, the Cauchy-Schwarz inequality and Bell's inequalities are prominent examples that have been put to scrutiny in a large and varied set of platforms. The Cauchy-Schwarz Inequality (CSI) is one of the most important relations in all of mathematics. It states that fluctuations of products of random variables are bounded by the product of autocorrelations:
Leggett-Garg tests of macrorealism for dynamical cat states evolving in a nonlinear medium
Physical Review A, 2019
We show violations of Leggett-Garg inequalities to be possible for single-mode cat-states evolving dynamically in the presence of a nonlinear quantum interaction arising from, for instance, a Kerr medium. In order to prove the results, we derive a generalised version of the Leggett-Garg inequality involving different cat-states at different times. The violations demonstrate failure of the premise of macro-realism as defined by Leggett and Garg, provided extra assumptions associated with experimental tests are valid. With the additional assumption of stationarity, violations of the Leggett-Garg inequality are predicted for the multi-component cat-states observed in the Bose-Einstein condensate and superconducting circuit experiments of Greiner et al. [Nature 419, 51, (2002)] and Kirchmair et al. [Nature, 495, 205 (2013)]. The violations demonstrate a mesoscopic quantum coherence, by negating that the system can be in a classical mixture of mesoscopically distinct coherent states. Higher orders of nonlinearity are also studied and shown to give strong violation of Leggett-Garg inequalities.