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Physical Review A

Decoherence in the collision of two Bose-Einstein condensates

Krzysztof Pawłowski, Kazimierz Rza̧żewski

Published Apr 27, 2009• 1 citation
Publisher

Abstract

Decoherence in simple experiments with Bose-Einstein condensates is of great importance for quantum engineering. We study a system of two colliding condensates in Fock and correlated states. During the collision some atoms are scattered out of the condensates, which leads to the decoherence. The quantum dynamics of the condensates is described by a master equation. In a simplified model we present analytical results. For more realistic conditions numerics is invoked. The depletion of the colliding condensates is accompanied by a decoherence.

DOI
10.1103/physreva.79.043628

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Decoherence in simple experiments with Bose-Einstein condensates is of great importance for quantum engineering. We study a system of two colliding condensates in Fock and correlated states. During the collision some atoms are scattered out of the condensates, which leads to the decoherence. The quantum dynamics of the condensates is described by a master equation. In a simplified model we present analytical results. For more realistic conditions numerics is invoked. The depletion of the colliding condensates is accompanied by a decoherence.
We propose a method for simulating a single realization of a collision of two Bose--Einstein condensates. Recently in Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) we introduced a quantum model of an incoherent elastic scattering in a collision of two counter-propagating atomic Gaussian wavepackets. Here show that this model is capable of generating the data that can be interpreted as results of a single collision event. We find a range of parameters, including relative velocity, population and the size of colliding condensates, where the structure of hallo of scattered atoms in a single realization strongly differs from that averaged over many realizations.
We propose a method for simulating a single realization of a collision of two Bose-Einstein condensates. Recently [Phys. Rev. Lett. 94, 200401 (2005)], we introduced a quantum model of incoherent elastic scattering in a collision of two counterpropagating atomic Gaussian wave packets. Here we show that this model is capable of generating data that can be interpreted as results of a single collisional event. We find a range of parameters, including relative velocity, population, and the size of colliding condensates, where the structure of the halo of scattered atoms in a single realization strongly differs from that averaged over many realizations.
During a collision of Bose-Einstein condensates correlated pairs of atoms are emitted. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of Einstein-Podolsky-Rosen correlations, or sub-shot-noise atomic interferometry. Usually, a theoretical description of the collision relies either on stochastic numerical methods or on analytical treatments involving various approximations. Here, we investigate elastic scattering of atoms from colliding elongated Bose-Einstein condensates within the Bogoliubov method, carefully controlling performed approximations at every stage of the analysis. We derive expressions for the one- and two-particle correlation functions. The obtained formulas, which relate the correlation functions to the condensate wave function, are convenient for numerical calculations. We employ the variational approach for condensate wave functions to obtain analytical expressions for the correlation functions, whose properties we analyze in detail. We also present a useful semiclassical model of the process and compare its results with the quantum one. The results are relevant for recent experiments with excited helium atoms, as well as for planned experiments aimed at investigating the nonclassicality of the system.
Bose-Einstein condensates (BEC) serve as a model system for the study of decoherence and dephasing processes. We denote ‘dephasing’ as the loss of overall common phase due to the coherent evo lution of the macroscopic wavefunction of the BEC. In contrast, ‘decoherence’ in this case is the coupling of the macroscopic wavefunction state to a continuum of initially unoccupied momentum excitations via collisions. Decoherence is driven by the fluctuations in th ese momentum modes and is irreversible on the timescales larger than the so -called ‘memory time’ of the continuum [1].
We analyze atom-atom correlations in the sss-wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear (CL) and back-to-back (BB) correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short-time limit are in agreement with the first-principles simulations using the positive-PPP representation and provide analytic insights into the experimental observations of Perrin et al. [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.
Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zi\ifmmode \acute{n}\else \'{n}\fi{} et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insight into correlation properties of scattered atoms.