The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the deformation of the classical flow by the quantum nonlinearity in the semiclassical limit. The breakdown of the classical trajectories under the quantum nonlinear dynamics is quantified by the mismatch of the quasi-flow carried by different observables. It is shown that the failure of classical realism can give rise to a dynamical violation of Bell's inequalities.
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. Since the harmonic oscillator dynamics admits a hidden trajectory formulation, the assumptions of macrorealism are violated only by the measurement process. We demonstrate a breakdown of macrorealism in a wide parameter range that is maximized in a scaling limit of extreme squeezing. A semiclassical analysis shows that macrorealism is violated even with measurements of classically smooth observables that do not resolve quantum levels. We propose an experimental test of macr…
The Dicke model, which describes the coupling of an ensemble of spins to a harmonic oscillator, is known for its superradiant phase transition, which can both be observed in the ground state in a purely Hamiltonian setting, as well as in the steady state of an open-system Dicke model with dissipation. We demonstrate that, in addition, the dissipative Dicke model can undergo a second phase transition to a nonstationary phase, characterized by unlimited heating of the harmonic oscillator. Identifying the mechanism of the phase transition and deriving the scaling of the critical coupling with the…
In this paper we study in details a system of two weakly coupled harmonic oscillators. This system may be viewed as a simple model for the interaction between a photon and a photodetector. We obtain exact solutions for the general case. We then compute approximate solutions for the case of a single photon (where one oscillator is initially in its first excited state) reaching a photodetector in its ground state (the other oscillator). The approximate solutions represent the state of both the photon and the photodetector after the interaction, which is not an eigenstate of the individual hamilt…
The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As an example harmonic oscillator potential is considered.
We study the fluctuations of the work performed on a driven quantum system, defined as the difference between subsequent measurements of energy eigenvalues. These work fluctuations are governed by statistical theorems with similar expressions in classical and quantum physics. In this article we show that we can distinguish quantum and classical work fluctuations, as the latter can be described by a macrorealistic theory and hence obey Leggett-Garg inequalities. We show that these inequalities are violated by quantum processes in a driven two-level system and in a harmonic oscillator subject to…
Fermi's golden rule applies to a situation in which a single quantum state $|ψ\rangle$ is coupled to a near-continuum. This "quasi-continuum coupling" structure results in a rate equation for the population of $|ψ\rangle$. Here we show that the coupling of a quantum system to the standard model of a thermal environment, a bath of harmonic oscillators, can be decomposed into a "cascade" made up of the quasi-continuum coupling structures of Fermi's golden rule. This clarifies the connection between the physics of the golden rule and that of a thermal bath, and provides a non-rigorous but physica…
The composition of the quantum potential and its role in the breakdown of classical symplectic symmetry in quantum mechanics is investigated. General expressions are derived for the quantum potential in both configuration space and momentum space representations. By comparing the configuration space and momentum space representations of the causal interpretation of quantum mechanics, the quantum potential is shown to break the symplectic symmetry that exists between these two representations in classical mechanics. In addition, it is shown that the quantum potential in configuration space may …
We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system; namely the absence of a joint probability distribution of the position $x$ and momentum $p$. Elaborating on a recently reported criterion by Bednorz and Belzig [Phys. Rev. A {\bf 83}, 52113] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using homodyne measurement of a single photon state, thus proving a straightforward signature of the breakdown …
We follow the passage from complex amplitude bistability to phase bistability in the driven dissipative Jaynes-Cummings oscillator. Quasidistribution functions in the steady state are employed, for varying qubit-cavity detuning and drive parameters, in order to track a first-order dissipative quantum phase transition up to the critical point marking a second-order transition and spontaneous symmetry breaking. We demonstrate the photon blockade breakdown in the dispersive regime, and find that the coexistence of cavity states in the regime of quantum bistability is accompanied by pronounced qub…
The Leggett-Garg inequality (LGI), based on the notions of realism and noninvasive measurability, is applied in the context of a linear harmonic oscillator. It is found that merely through observing at various instants which region of the potential well, the oscillating quantum object is in, the LGI can be violated without taking recourse to any ancillary quantum system. Strikingly, this violation reveals an unexplored nonclassicality of the state which is considered the most "classical-like" of all quantum states, namely the Schrödinger coherent state. In the macrolimit, the extent to which s…
Quantum experiments with nanomechanical oscillators are regarded as a testbed for hypothetical modifications of the Schrödinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macro-scale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes f…
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from some of the most fundamental concepts of classical physics - in particular that properties of an object are well defined independent of measurements (realism) and only affected by local interactions (locality). The violation of these bounds unambiguously shows that the measured system does not behave classically, void of any assumption on the validity of quantu…
The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the …
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process predicted for an adiabatic encircling of an exceptional point. In this work we analyse this and related processes for the generic system of two coupled oscillator modes with loss or gain. We identify a characteristic system evolution consisting of periods of quasi-stationarity interrupted by abrupt non-adiabatic transitions, and we present a qualitative and quant…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict attention to a system of…
Ultrafast chemical reactions are difficult to simulate because they involve entangled, many-body wavefunctions whose computational complexity grows rapidly with molecular size. In photochemistry, the breakdown of the Born-Oppenheimer approximation further complicates the problem by entangling nuclear and electronic degrees of freedom. Here, we show that analog quantum simulators can efficiently simulate molecular dynamics using commonly available bosonic modes to represent molecular vibrations. Our approach can be implemented in any device with a qudit controllably coupled to bosonic oscillato…
