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Conference on Lasers and Electro-Optics

Measuring the multiparticle state of a two-mode Bose-Einstein condensate

Eric L. Bolda, S. M. Tan, Daniel F. Walls

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given. Much recent interest in the new dilute alkali Bose-Einstein condensate sytems from the idea that the multiparticle state may be highly squeezed due to collisions. The internal states of the atoms can serve as a probe of this squeezing. Motivated by the success of homodyne tomography in measuring the quantum state of light, we propose to obtain the complete density matrix of a two-mode condensate from repeated atom-counting measurements.

DOI
10.1109/iqec.1998.680320

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Summary form only given. Much recent interest in the new dilute alkali Bose-Einstein condensate sytems from the idea that the multiparticle state may be highly squeezed due to collisions. The internal states of the atoms can serve as a probe of this squeezing. Motivated by the success of homodyne tomography in measuring the quantum state of light, we propose to obtain the complete density matrix of a two-mode condensate from repeated atom-counting measurements.
We describe an atomic interferometer based on Raman transitions between two hyperfine states. We show how atom count probabilities at the output of the interferometer can be used to reconstruct the joint multiparticle state of a two-mode Bose-Einstein condensate. Two data collection schemes are compared, via numerical solution for the density matrix from the probability data and analytical estimates of the errors are made. In the first scheme, only the phase of the interferometer is varied. We prove that state reconstruction is impossible for the case of a balanced beam splitter; otherwise, the problem is ill-conditioned. In the second scheme, both the phase and transmission parameters are varied, the QQQ function can be measured directly, and the reconstruction of the state is well conditioned.
Summary form only given. Following the first observations of Bose-Einstein condensation (BEC) in dilute atomic gases, there has been considerable interest in multiple condensates as a system of interpenetrating quantum fluids. Most recently in our time averaged orbiting potential (TOP) trap, we have created coherent superpositions of condensates in the |F=1, m/sub F/=-1> and |F=2, m/sub F/=1> hyperfine ground states of Rubidium-87. A coupling field connects the states of this two level system. Following evaporative cooling to BEC in the |1,-1> state, a short coupling pulse allows us to transfer an arbitrary proportion of the atoms into the upper |2,1> state. In the first experiments with two component condensates, we have determined the ratio of the intraspecies scattering lengths for the two hyperfine states mentioned above; we have transferred half of the atoms to the upper |2,1> state to investigate the dynamics of the two components separation; and we have found that, in the regions where they overlap, the two condensates retain a well defined phase even after the damping of their relative center of mass motion. To further our studies of double condensates, we have implemented a new, state-sensitive form of nondestructive imaging, a technique first pioneered by Zernike in the field of microscopy, and more recently adapted to the imaging of condensates by the group at MIT. We exploit the state sensitivity of the technique to distinguish the two spin states inside the trap (or, more accurately, to measure their relative density across the cloud).
Spin changing collisions in alkaline Bose-Einstein condensates can be employed to generate highly entangled atomic quantum states. Here, we will report on the generation of two classes of entangled states. Firstly, we demonstrate the generation of two-mode squeezed vacuum states and record their characteristic quadrature correlations by atomic homodyning. We prove that the correlations fulfill Reid’s criterion [1] for continuous-variable Einstein-Podolsky-Rosen entanglement. The homodyne measurements allow for a full tomographic reconstruction, yielding a two-mode squeezed state with a 78% fidelity. The created state can be directly applied to atom interferometry, as is exemplified by an atomic clock measurement beyond the Standard Quantum Limit. Secondly, we demonstrate entanglement between two spatially separated atomic modes. The entangled state is obtained by spatially splitting a Twin Fock state of indistinguishable atoms along a line of zero density. This structure of two separated atomic modes is obtained by utilizing an excited trap mode. The non-classical correlations between these atomic modes are verified by applying a novel entanglement criterion especially sensitive for our case. The method opens a path to exploit the recent success in the creation of many-particle entanglement in ultracold atoms for the field of quantum information, where individually addressable subsystems are required. Finally, we will show how the measurement protocol can be extended to perform a Bell test of quantum nonlocality. [1] M. Reid, Phys. Rev. A 40, 913-923 (1989)
We study the limitations for entanglement due to collisional decoherence in a Bose-Einstein condensate. Specifically we consider relative number squeezing between photons and atoms coupled out from a homogeneous condensate. We study the decay of excited quasiparticle modes due to collisions in condensates of atoms with one or two internal degrees of freedom. The time evolution of these modes is determined in the linear response approximation to the deviation from equilibrium. We use Heisenberg-Langevin equations to derive equations of motion for the densities and higher correlation functions which determine the squeezing. In this way we can show that decoherence due to quasiparticle interactions imposes an important limit on the degree of number squeezing which may be achieved. Our results are also relevant for the determination of decoherence times in other experiments based on entanglement, e.g. the slowing and stopping of light in condensed atomic gases using dark states.