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Physical Review A

Creation, detection, and decoherence of macroscopic quantum superposition states in double-well Bose-Einstein condensates

Yixiao Huang, M. G. Moore

Published Feb 7, 2006• 82 citations
Publisher

Abstract

We study the possibility of creating many-particle macroscopic quantum superposition (Schr\"odinger cat)--like states by using a Feshbach resonance to reverse the sign of the scattering length of a Bose-Einstein condensate trapped in a double-well potential. To address the issue of the experimental verification of coherence in the catlike state, we study the revival of the initial condensate state in the presence of environmentally induced decoherence. As a source of decoherence, we consider the interaction between the atoms and the electromagnetic vacuum, due to the polarization induced by an incident laser field. We find that the resulting decoherence is directly related to the rate at which spontaneously scattered photons carry away sufficient information to distinguish between the two atom distributions which make-up the cat state. We show that for a ``perfect'' cat state, a single scattered photon will bring about a collapse of the superposition, while a less-than-perfect catlike state can survive multiple scatterings before the collapse occurs. In addition, we study the dephasing effect of atom-atom collisions on the catlike states.

DOI
10.1103/physreva.73.023606

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We study the possibility of creating many-particle macroscopic quantum superposition (Schr"odinger cat)--like states by using a Feshbach resonance to reverse the sign of the scattering length of a Bose-Einstein condensate trapped in a double-well potential. To address the issue of the experimental verification of coherence in the catlike state, we study the revival of the initial condensate state in the presence of environmentally induced decoherence. As a source of decoherence, we consider the interaction between the atoms and the electromagnetic vacuum, due to the polarization induced by an incident laser field. We find that the resulting decoherence is directly related to the rate at which spontaneously scattered photons carry away sufficient information to distinguish between the two atom distributions which make-up the cat state. We show that for a ``perfect'' cat state, a single scattered photon will bring about a collapse of the superposition, while a less-than-perfect catlike state can survive multiple scatterings before the collapse occurs. In addition, we study the dephasing effect of atom-atom collisions on the catlike states.
We study the possibility to create many-particle Schrödinger cat-like states by using a Feshbach resonance to reverse the sign of the scattering length of a Bose-Einstein condensate trapped in a double-well potential. To address the issue of experimental verification of coherence in the cat-like state, we study the revival of the initial condensate state in the presence of environmentally-induced decoherence. As a source of decoherence, we consider the interaction between the atoms and the electromagnetic vacuum, due to the polarization induced by an incident laser field. We find that the resulting decoherence is directly related to the rate at which spontaneously scattered photons carry away sufficient information to distinguish between the two atom-distributions which make-up the cat state. We show that for a 'perfect' cat-state, a single scattered photon will bring about a collapse of the superposition, while a less-than-perfect cat-like state can survive multiple scatterings before collapse occurs. In addition, we study the dephasing effect of atom-atom collisions on the cat-like states.
We consider a quantum superposition of Bose-Einstein condensates (BEC's) in two immiscible internal states. A decoherence rate for the resulting Schr\"odinger cat is calculated and shown to be a significant threat to this macroscopic quantum superposition of BEC's. An experimental scenario is outlined where the decoherence rate due to the thermal cloud is dramatically reduced thanks to trap engineering and ``symmetrization'' of the environment, which allow the Schr\"odinger cat to be an approximate pointer state.
Quantum superpositions of macroscopically distinguishable states having distinct phases can be created with a Bose-Einstein condensate trapped in a periodic potential. The experimental signature is contained in the phase distribution of the interference patterns obtained after releasing the traps. Moreover, in the double-well case, this distribution exhibits a dramatic dependence on the parity of the total number of atoms. We finally show that, for single-well occupations up to a few hundred atoms, the macroscopic quantum superposition can be robust enough against decoherence to be experimentally revealable within current technology.
We study theoretically the interaction-induced generation of mesoscopic coherent spin state superpositions (small-particle-number cat states) from an initial coherent spin state in bimodal Bose-Einstein condensates and the subsequent phase revival, including decoherence due to particle losses and fluctuations of the total particle number. In a full multimode description, we propose a preparation procedure of the initial coherent spin state and we study the effect of preexisting thermal fluctuations on the phase revival, and on the spin and orbito-spinorial cat-state fidelities.
Can macroscopic quantum superposition states (or highly entangled number states) be observed directly'? Specifically, can phase contrast imaging be applied to observe a superposition state with essentially "all" of the atoms in a gaseous double well BEG being simultaneously in both wells at the same time'? That is we are looking to image states of the type vertical bar N, 0 > +vertical bar 0, N > where vertical bar L, R > denotes L particles in the Left well and R. in the Right. We will happily settle for states of the form IN n, n > +In, N is >, with 71, << N, these being less ephemeral. Earlier work in our group, Perry, Reinhardt and Kahn, has shown that such highly entangled number states may be generated by appropriate phase engineering, just as in the case of the phase engineering of solitons in single well BECs. Experimentalists have been hesitant to attempt to create such states in fear that definitive observations cannot be carried out. There have also been suggestions that "Nature" will prevent such superpositions from existing for N too large... and thus there are also basic issues in quantum theory which may prevent the formation and detection of such states. In the present progress report we begin an investigation of calculating the lifetimes of such entangled states in the presence of both observation and spontaneous decay both of which perturb, and eventually destroy, the entanglement under investigation via quantum back-action. Quantum State Diffusion (QSD) provides a useful computational tool in addressing such questions, and we present the initial results of exploring this novel use of QSD.
We consider a Bose-Einstein condensate of 7Li{}^{7}\mathrm{Li}7Li in a situation where the density undergoes a symmetry breaking in real space. This occurs for a suitable number of condensed atoms in a double-well potential, obtained by adding a standing-wave light field to the trap potential. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation leads, in fact, to a macroscopic quantum superposition or Schr\"odinger cat (SC) and evaluate the tunneling rate between the two SC states. The oscillation between the two states is called macroscopic quantum coherence (MQC); we study the effects of losses on MQC.