Measurement-induced squeezing of a Bose-Einstein condensate

Abstract

We discuss the dynamics of a Bose-Einstein condensate during its nondestructive imaging. A generalized Lindblad superoperator in the condensate master equation is used to include the effect of the measurement. A continuous imaging with a sufficiently high laser intensity progressively drives the quantum state of the condensate into number squeezed states. Observable consequences of such a measurementinduced squeezing are discussed. 03.75.Fi, 42.50.Md Since its birth, quantum mechanics has led to an interpretational debate on the role played by the measurement process in its structure and its relationship to classical mechanics developed for macroscopic systems [1]. This debate has been enriched by the realization of new experimental techniques spanning from quantum jumps in single ion traps to macroscopic entangled states in various quantum systems. Recently, the production of atomic Bose-Einstein condensates of dilute atomic gases has also paved the way to the study of dynamical phenomena of macroscopic quantum systems with the precision characteristic of atomic physics [2].Two optical techniques, absorption and dispersive imagings, have been used to monitor the dynamics of a Bose-Einstein condensate [2]. In the former the condensate interacts with a light beam resonant (or close to resonance) with an atomic transition. The output beam is attenuated proportionally to the column density of the condensate -the condensate density integrated along the line of sight of the imaging beam. The absorption of photons heats the condensate then strongly perturbing it, and in general a new replica of the condensate has to be produced to further study its dynamics. This measurement is, in the language of quantum measurement theory, of type-II since it destroys the state of the observed system and forbids the study of the dynamics of a single quantum system [3]. Repeated measurements on a Bose-Einstein condensate or, at the limit, its continuous monitoring are instead possible using its dispersive features, for instance through phase-contrast [4] or interference [5] imaging techniques. Off-resonance light is scattered by the condensate which induces phase-shifts thereby converted into light intensity modulations by homodyne or heterodyne detection. The off-resonant nature of the atom-photon interaction allows for a very low absorption rate and therefore low heating of the condensate. Thus, multiple shots of the same condensate can be taken -a type-I measurement -allowing to study with high accuracy several phenomena, like its formation in non-adiabatic conditions [6], short and long wavelength collective excitations [7], vortices and superfluid dynamics [8]. The effect of the measurement process is typically neglected in these analysis. A first attempt to include the measurement process in a two-mode configuration for the condensate has been discussed in [9]. Our main goal is to include the atom-photon interaction process present in dispersive imaging into the intrinsic dynamics of the condensate. We show that the measure...

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

“…It would be particularly interesting to explore how classical approximations make dynamical trajectories more objective than their fully-quantum mechanical counterparts and whether our classical measurement trajectories are affected by the choice of measurement scheme, such as photon counting, homodyne or heterodyne measurements [27,91]. The backaction of homodyne measurements has been studied for simplified models of BECs in cavities [92], in dispersive imaging [49,93], and in an interferometric context [94] (related to the experiments of Ref. [95]); the photon counting of scattered light was simulated in Refs.…”

Continuous quantum measurement of a Bose-Einstein condensate: A stochastic Gross-Pitaevskii equation

“…This has already been described in detail elsewhere [17], thus here we only summarize the main results and their link to the following considerations. By neglecting the depletion term, the master equation for the condensate takes the forṁ…”

“…In Section III we unravel the Lindblad equation in terms of a stochastic differential equation that, in the unmeasured case, corresponds to the description of a single N-body wavefunction. A solution of the stochastic N-body equation is discussed in the limit of strong continuous measurement, leading to the squeezing of number fluctuations, the main result described in [17]. In the opposite limit of weak measurement and for an initial mean-field state this stochastic equation becomes the stochastic counterpart of the Gross-Pitaevskii equation, as discussed in Section IV.…”

“…In this paper we try to answer the question formulated above by building a realistic model for dispersive measurements of the condensate, extending the results reported in [17] to the weak measurement regime. The plan of the paper is as follows.…”

Continuous measurement of atom-number moments of a Bose-Einstein condensate by photodetection

“…Previous treatments on BEC continuous measurements have been described in Refs. [9][10][11][12], differing considerably from our approach and goals. We consider a BEC trapped inside a ring-cavity fed by two resonant (orthogonaly polarized) propagating fields -an undepleted probe and a weak quantum probe field (Fig.1).…”