We propose a method to construct a classical analog of an open quantum system, namely a single quantum particle confined in a potential well and immersed in a thermal bath. The classical analog is made out of a collection of identical wells where classical particles of mass $m$ are trapped. The distribution $n(x,t)$ of the classical positions is used to reconstruct the quantum Bohm potential $V_{\rm Bohm} = -\frac{\hbar^2}{2 m} \frac{Δ\sqrt{n}}{\sqrt{n}}$, which in turn acts on the shape of the potential wells. As a result, the classical particles experience an effective "quantum" force. This protocol is tested with numerical simulations using single- and double-well potentials, evidencing typical quantum effects such as long-lasting correlations and quantum tunneling. For harmonic confinement, the analogy is implemented experimentally using micron-sized dielectric beads optically trapped by a laser beam.
I expose nonrelativistic quantum electrodynamics in the Weyl-Wigner representation. Hence I prove that an approximation to first order in Planck constant has formal analogy with stochastic electrodynamics (SED), that is classical electrodynamics of charged particles immersed in a random radiation filling space. The analogy elucidates why SED agrees with quantum theory for particle Hamiltonians quadratic in coordinates and momenta, but fails otherwise.
We discuss how continuous probing of a quantum system allows estimation of unknown classical parameters embodied in the Hamiltonian of the system. We generalize the stochastic master equation associated with continuous observation processes to a Bayesian filter equation for the probability distribution of the desired parameters, and we illustrate its application by estimating the direction of a magnetic field. In our example, the field causes a ground state spin precession in a two-level atom which is detected by the polarization rotation of off-resonant optical probes, interacting with the at…
We analyze the performance of a protocol to prepare an atomic ensemble in a superposition of two macroscopically distinguishable states. The protocol relies on conditional measurements performed on a light field, which interacts with the atoms inside an optical cavity prior to detection, and we investigate cavity enhanced probing with continuous beams of both coherent and squeezed light. The stochastic master equations used in the analysis are expressed in terms of the Hamiltonian of the probed system and the interaction between the probed system and the probe field and are thus quite generall…
In magnetism, skyrmions correspond to classical three-dimensional spin textures characterized by a topological invariant that keeps track of the winding of the magnetization in real space, a property that cannot be easily generalized to the quantum case since the orientation of a quantum spin is in general ill-defined. Moreover, as we show, the quantum skyrmion state cannot be directly observed in modern experiments that probe the local magnetization of the system. However, we show that this novel quantum state can still be identified and fully characterized by a special local three-spin corre…
We theoretically propose an experimentally viable scheme to use an impurity atom in a dipolar Bose-Einstein condensate (BEC), in order to probe analogue low-energy Lorentz violation from the modified dispersion at high energies as suggested by quantum theories of gravity. We show that the density fluctuations in the dipolar BEC possess a Lorentz-violating Bogoliubov spectrum $ω_\mathbf{k}=c_0|\mathbf{k}|f(c_0|\mathbf{k}|/M_\star)$, with recovery of approximate Lorentz invariance (LI) at energy scales much below $M_\star$. When $f$ is adjusted to dip below unity somewhere, the impurity, analogo…
The quantum hydrodynamic like equations as a function of two real sets of variables, the 4x4 action matrix and the 4 dimensional wave function modulus vector of the Dirac equation, are derived in the present work. The paper shows that in the low velocity limit the equations lead to the hydrodynamic representation of the Pauli equation for charged particle with spin given by Janossy and by Bialynicki.The Lorentz invariance of the relativistic quantum potential that generates the non-local behavior of the quantum mechanics is discussed.
In the present paper the gas, liquid and solid phases made of structureless particles, are visited to the light of the quantum stochastic hydrodynamic analogy (SQHA). The SQHA shows that the open quantum mechanical behavior is maintained on a distance shorter than the theory-defined quantum correlation length (lc). When, the physical length of the problem is larger than lc, the model shows that the quantum (potential) interactions may have a finite range of interaction maintaining the non-local behavior on a finite distance quantum non-locality length lq. The present work shows that when the m…
The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the weak value in the quantum mechanics. A negative probability and abnormal expectations of some quantities remarkablely larger than their inherent norms are found in an example of a stochastic Ising spin system.
We propose experimental protocols to reveal thermoelectric and thermal effects in the transport properties of ultracold fermionic atoms, using the two-terminal setup recently realized at ETH. We show in particular that, for two reservoirs having equal particle numbers but different temperatures initially, the observation of a transient particle number imbalance during equilibration is a direct evidence of thermoelectric (off-diagonal) transport coefficients. This is a time-dependent analogue of the Seebeck effect, and a corresponding analogue of the Peltier effect can be proposed. We reveal th…
This approach to the incorporation of stochastic thermodynamics into quantum theory is based on the conception of consistent inclusion of the holistic stochastic environmental influence described by wave functions of the arbitrary vacuum, which was proposed in our paper previously. In this study, we implement the possibility of explicitly incorporating the zeroth law of stochastic thermodynamics in the form of the saturated Schrödinger uncertainty relation into quantum theory. This allows comparatively analyzing the sets of states of arbitrary vacuums, namely, squeezed coherent states (SCSs) a…
We investigate the position oscillation of a particle that models the center of mass quantum state of a trapped Bose-Einstein condensate coupled to the zero-point fluctuations of the gravitational field. A semiclassical analysis is performed that allows to calculate the mean square amplitude of the oscillation. In analogy with the Lamb shift in quantum electrodynamics, this gives rise to an upshift of the energy of the trapped condensates. We show that for an elongated trap, the energy shift scales quadratically with the length as well as cubically with the total number of atoms.
One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known symmetrized form of the master equation, which is formally equivalent to the wave equation in quantum mechanics apart from the fact that wave functions are always real. The origin of the unusual behaviors of the weak value such as the negative probability and the abnormal enhancement of some expectations becomes clearer in the present case, where the two-time conditio…
The lambda point in liquid He4 is a well established phenomenon acknowledged as an example of Bose-Einstain condensation. This is generally accepted, but there are serious discrepancies between the theory and experimental results, namely the lower value of the transition temperature Tl and the negative value of dTl /dP. These discrepancies can be explained in term of the quantum stochastic hydrodynamic analogy (QSHA). The QSHA shows that at the He4I\textregisteredHe4II superfluid transition the quantum coherence length lc becomes of order of the distance up to which the wave function of a coup…
The Unruh effect states an accelerated particle detector registers a thermal response when moving through the Minkowski vacuum, and its thermal feature is believed to be inseparable from Lorentz symmetry: Without the latter, the former disappears. Here we propose to observe analogue circular Unruh effect using an impurity atom in a quasi-two-dimensional Bose-Einstein condensate (BEC) with dominant dipole-dipole interactions between atoms or molecules in the ultracold gas. Quantum fluctuations in the condensate possess a Bogoliubov spectrum $ω_{\mathbf k}=c_0|{\mathbf k}|f(\hbar\,c_0|{\mathbf k…
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling tra…
In this work we examine the effect of phase-space noncommutativity on some typically quantum properties such as quantum beating, quantum information, and decoherence. To exemplify these issues we consider the two-dimensional noncommutative quantum harmonic oscillator whose components behavior we monitor in time. This procedure allows us to determine how the noncommutative parameters are related to the missing information quantified by the linear quantum entropy and by the mutual information between the relevant Hilbert space coordinates. Particular questions concerning the thermodynamic limit …
