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arXiv:cond-mat/0007217 · Physical Review A

Orthogonality catastrophe and decoherence of a confined Bose-Einstein condensate at finite temperature

Anatoly B. Kuklov, Joseph L. Birman

Published Dec 12, 2000• 15 citations
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Abstract

We discuss the mechanisms of decoherence of a confined Bose-Einstein condensate at finite temperatures under the explicit condition of conservation of the total number of bosons, N, in the trap. A criterion for the irreversible decay of the condensate two-time correlator is formulated in terms of the orthogonality catastrophe (OC) for the exact N-body eigenstates, so that no irreversible decay occurs without the OC. If an infinite external bath contacts a finite condensate, the OC should practically always occur as long as the bath degrees of freedom are interacting with each other. We find that, if no external bath is present and the role of the bath is played by the normal component, no irreversible decay occurs. We discuss the role of the effect of level repulsion in eliminating the OC. At finite temperatures, the time correlations of the condensate isolated from the environment are dominated by reversible dephasing which results from the thermal ensemble averaging over realizations of the normal component. Accordingly, the correlator exhibits Gaussian decay with a certain decay time ${\ensuremath{\tau}}_{d}$ which depends on the temperature as well as on the intensity of the shot noise determined by the statistical uncertainty in the number of bosons, N, in the trap.

DOI
10.1103/physreva.63.013609

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arXiv:cond-mat/9611207•Physical Review A•May 1, 1997•8 citations
We discuss the mechanisms of decoherence of a confined Bose-Einstein condensate at finite temperatures under the explicit condition of conservation of the total number of bosons, N, in the trap. A criterion for the irreversible decay of the condensate two-time correlator is formulated in terms of the orthogonality catastrophe (OC) for the exact N-body eigenstates, so that no irreversible decay occurs without the OC. If an infinite external bath contacts a finite condensate, the OC should practically always occur as long as the bath degrees of freedom are interacting with each other. We find that, if no external bath is present and the role of the bath is played by the normal component, no irreversible decay occurs. We discuss the role of the effect of level repulsion in eliminating the OC. At finite temperatures, the time correlations of the condensate isolated from the environment are dominated by reversible dephasing which results from the thermal ensemble averaging over realizations of the normal component. Accordingly, the correlator exhibits Gaussian decay with a certain decay time \ensuremathτd{\ensuremath{\tau}}_{d}\ensuremathτd​ which depends on the temperature as well as on the intensity of the shot noise determined by the statistical uncertainty in the number of bosons, N, in the trap.
Implications of the internal symmetries on the dynamics of the trapped two-component atomic vapors are discussed. In the cases of 87^{87}87Rb (bosons) as well as of 40^{40}40K (fermions) trapped in the two hyperfine states, the intrinsic su(2)su(2)su(2) symmetry can be realized with a very good precision. Such a symmetry protects the global operators, which are the generators of the symmetry, from any decoherence. The case of boson-fermion mixture is discussed as well. The role of external factors, breaking the symmetry, in inducing the decoherence of the global operators is considered. It is shown that, the loss of the correlations is not faster than the rates of the induced heating or losses, provided the noise is characterized by short correlation length. The case of the extrinsic long-ranged fluctuations is also considered. Intrinsic mechanisms of decoherence of the correlators of the condensate operators of the two-component condensate are analyzed. The atomic echo is discussed as a test for the reversibility of the phase diffusion effect. The intensity and the profile of the multiple echo are calculated numerically as well as analytically.
The conventional conception of decoherence relies on the interaction with an external set of degrees of freedom - the 'bath' - to which the system loses quantum information. But the role of the bath can be played too by any internal degrees of freedom that are not accessible to the observer, and in this sense we can talk about 'Self-Induced Decoherence'. Simulating the exact time-evolution of the few-body Bose-Hubbard Hamiltonian, we provide numerical evidence of the decay of quantum purity in the sense of 'temporal typicality' referred in the context of pure state Quantum Statistical Mechanics. We analyse the causes of such purity loss in terms of the structural differences of the interacting many-body Hamiltonian in comparison with its non-interacting counterpart, finding that the predominant role in the long term behaviour is played by the shifts in the many-body energy spectrum.
Thermal fluctuations of the normal component induce dephasing---reversible damping of the low-energy collective modes of a confined Bose-Einstein condensate. The dephasing rate is calculated for the isotropic oscillator trap, where the Landau damping is expected to be suppressed. This rate is characterized by a steep temperature dependence. It is weakly amplitude dependent, and is sensitive to the total number of atoms in the trap. The value of the rate belongs to the range of the damping rates observed by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)]. We suggest that a reversible nature of the damping caused by the thermal dephasing in the isotropic trap can be tested by the echo effect. A reversible nature of the Landau damping is also discussed, and a possibility of observing the echo effect in an anisotropic trap is considered as well. The parameters of the echo for the isotropic trap are calculated in the weak echo limit. Results of the numerical simulations of the echo are also presented.
We examine the time evolution of cold atoms (impurities) interacting with an environment consisting of a degenerate bosonic quantum gas. The impurity atoms differ from the environment atoms, being of a different species. This allows one to superimpose two independent trapping potentials, each being effective only on one atomic kind, while transparent to the other. When the environment is homogeneous and the impurities are confined in a potential consisting of a set of double wells, the system can be described in terms of an effective spin-boson model, where the occupation of the left or right well of each site represents the two (pseudo)-spin states. The irreversible dynamics of such system is here studied exactly, i.e. not in terms of a Markovian master equation. The dynamics of one and two impurities is remarkably different in respect of the standard decoherence of the spin-boson system. In particular, we show: (i) the appearance of coherence oscillations, (ii) the presence of super and subdecoherent states that differ from the standard ones of the spin-boson model, and (iii) the persistence of coherence in the system at long times. We show that this behaviour is due to the fact that the pseudospins have an internal spatial structure. We argue that collective decoherence also prompts information about the correlation length of the environment. In a one-dimensional (1D) configuration, one can change even more strongly the qualitative behaviour of the dephasing just by tuning the interaction of the bath.
Summary form only given.We use quantum kinetic theory to calculate the steady-state and the fluctuations of a trapped Bose-Einstein condensate at finite temperature. We divide the system into two parts. The first part consists of the condensate particles. They are described quantum mechanically using the number-conserving Bogoliubov method that allows us to characterize the condensate by the number of condensed particles. The second part are the noncondensed particles. They are treated as a classical gas in thermal equilibrium. Using quantum kinetic theory we find a master equation for the reduced density operator of the Bose-Einstein condensate. We calculate the steady-state of the system and investigate the effect of one-, two- and three-particle losses on the condensate. Using linearized Ito equations we find expressions for the intensity fluctuations and the amplitude fluctuations in the condensate. The effect of the trap losses on the particle statistics is also studied. We then assume that the condensate particles are coherently pumped into an untrapped internal energy level and fall down in gravity. For this situation we derive the relation between the statistics of the trapped condensate particles and the statistics of the particles arriving at an atom detector positioned below the condensate.
Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles can demonstrate the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode, and N. The corresponding time values have been derived analytically under certain approximations and numerically for the parabolic atomic trap. The revival of the mode amplitude at a time of several seconds, as direct evidence of the effect, can occur if the normal component is significantly suppressed.