Classical stochastic measurement trajectories: Bosonic atomic gases in an optical cavity and quantum measurement backaction

Abstract

We formulate computationally efficient classical stochastic measurement trajectories for a multimode quantum system under continuous observation. Specifically, we consider the nonlinear dynamics of an atomic BoseEinstein condensate contained within an optical cavity subject to continuous monitoring of the light leaking out of the cavity. The classical trajectories encode within a classical phase-space representation a continuous quantum measurement process conditioned on a given detection record. We derive a Fokker-Planck equation for the quasiprobability distribution of the combined condensate-cavity system. We unravel the dynamics into stochastic classical trajectories that are conditioned on the quantum measurement process of the continuously monitored system. Since the dynamics of a continuously measured observable in a many-atom system can be closely approximated by classical dynamics, the method provides a numerically efficient and accurate approach to calculate the measurement record of a large multimode quantum system. Numerical simulations of the continuously monitored dynamics of a large atom cloud reveal considerably fluctuating phase profiles between different measurement trajectories, while ensemble averages exhibit local spatially varying phase decoherence. Individual measurement trajectories lead to spatial pattern formation and optomechanical motion that solely result from the measurement backaction. The backaction of the continuous quantum measurement process, conditioned on the detection record of the photons, spontaneously breaks the symmetry of the spatial profile of the condensate and can be tailored to selectively excite collective modes.

Collective dynamics of multimode bosonic systems induced by weak quantum measurement

“…, where W d is a Wiener increment representing the fluctuations in the photoncounts around the average value [65,76,77]. Substituting this expression in (76)- (81) we findˆˆ(…”

Exact classical stochastic representations of the many-body quantum dynamics

“…Then, we sample the initial conditions λ (t = 0) for the stochastic process (10) from the initial probability P (λ, t = 0) using the importance sampling method [29]. Each sampled initial condition λ (t = 0) is propagated in time by the numerical integration of the stochastic differential equation (10). The average value of the observable ô (t) at a time t is evaluated as the classical expectation ô (t) = E [O (λ (t))] over an ensemble of trajectories λ (t).…”

“…The field of research, which is the subject of such an activity, is truly interdisciplinary: quantum optics [4], utracold atoms in traps [5][6][7], quantum phase transitions [8], open quantum systems [9], and the measurement theory [10]. The motivation behind such studies range from purely practical (to provide exact data in order to verify a theory, or in order to interpret an experiment) to fundamental (to characterize the relationship between the classical and quantum computational complexity).…”

Engineering many-body dynamics with quantum light potentials and measurements

“…Uniting these fields [4,5] broadens both, and goes beyond the cases when either the light or matter are treated classically. Experimental [6][7][8][9][10][11] and theoretical works in this regime have revealed many interesting phenomena, such as the preparation of atomic states and dynamics [12][13][14][15][16][17][18][19], non-destructive measurement [20][21][22][23][24], many-body light-matter entanglement [23], self-organisation, and other new quantum phases [25][26][27][28][29][30][31][32][33][34][35][36].…”