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arXiv:cond-mat/9712282 · Physical Review A

Homodyne measurements on a Bose-Einstein condensate

Joel Frederick Corney, Gerard J Milburn

Published Sep 1, 1998• 54 citations
arXivHTMLPDF

Abstract

We investigate a nondestructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement backaction noise alone.

DOI
10.1103/physreva.58.2399

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We investigate a nondestructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement backaction noise alone.
The properties of an atomic Bose-Einstein condensate in a double-well potential are investigated through a two-mode analysis. An analytic solution for the semiclassical tunnelling and self-trapping dynamics is compared with numerical simulations of the quantum dynamics, which exhibit collapses and revivals for a closed system. A continuous non-destructive measurement technique to monitor the Josephson tunnelling oscillations is presented, in which the condensate in one well dispersively shifts the phase of a coherent probe beam in proportion to atom-number. The evolution of the resulting homodyne photocurrent and Bloch Q distributions shows that oscillations develop even when the initial state possesses phase symmetry. The conditional dynamics of the condensate which result from measurement back-action also appear in certain semiclassical formulations. The homodyne measurement technique is incorporated into a proposed weak-force detector. A maximally entangled initial state, which is the ground state for a double condensate with strong attractive atomic interactions, enables a high-precision measurement. The dynamics of quantum many-body multimode systems of interacting bosons are simulated using phase-space methods. The use of the Wigner technique predicts novel noise effects in fibre solitons. The positive-P representation is used to simulate the formation of mesoscopic Bose-Einstein condensates via evaporative cooling in three dimensional atom traps. The results indicate highly non-classical behaviour near the critical point, and provide evidence for the spontaneous formation of vortices. Comparisons with corresponding mean-field calculations reveal large differences between the semiclassical and fully quantum results. Finally, the possibility of future progress with alternative phase-space methods is considered.
The dynamics of a two-mode Bose-Einstein condensate trapped in a double-well potential results approximately in an effective Rabi oscillation regime of exchange of population between both wells for sufficiently strong overlap between the modes functions and sufficiently large condensates. Facing the effective Rabi oscillation as a temporal atomic beam splitter we propose a nondestructive measurement process allowing an atomic homodyne detection, thus yielding indirect relative phase information about one of the two-mode condensates. This proposal is achieved through a secondary optical homodyne detection, in which the field is allowed to dispersively interact with one of the condensate modes inside an optical cavity.
A scheme is proposed, that allows one for performing homodyne detection of the matter-wave field of ultracold bosonic atoms. It is based on a pump-probe lasers setup, that both illuminates a Bose-Einstein condensate, acting as reference system, and a second ultracold gas, composed by the same atoms but in a quantum phase to determine. Photon scattering outcouples atoms from both systems, which then propagate freely. Under appropriate conditions, when the same photon can either be scattered by the Bose-Einstein condensate or by the other quantum gas, both flux of outcoupled atoms and scattered photons exhibit oscillations, whose amplitude is proportional to the condensate fraction of the quantum gas. This setup allows one, for instance, to perform thermometry of a condensate or to monitor the Mott-insulator/superfluid phase transition in optical lattices, and can be extended in order to measure the first-order correlation function of a quantum gas. The dynamics here discussed make use of the entanglement between atoms and photons, which is established by the scattering process, in order to access detailed information on the quantum state of matter.
We study the interaction of light with two Bose-Einstein condensates as an open quantum system. The two overlapping condensates occupy two different Zeeman sublevels and two driving light beams induce a coherent quantum tunneling between the condensates. We derive the master equation for the system. It is shown via stochastic simulations that the measurements of spontaneously scattered photons establish the relative phase between two Bose-Einstein condensates, even though the condensates are initially in pure number states. These measurements are nondestructive for the condensates, because only light is scattered and no atoms are removed from the system. Due to macroscopic quantum interference the detection rate of photons depends strongly on the relative phase between the condensates. This may provide a way to distinguish between initial number states and initial symmetry-breaking states of the condensates.
Summary form only given. We present a potential scheme to detect weak forces by employing a BEC confined in a double-well potential. Initially the condensate is prepared in a coherent superposition of having all the atoms in one well or the other. We allow the condensate to experience a phase shift for a certain time /spl tau/ under the influence of the force. The phase shift can be detected by using the technique analogous to the Ramsey interference. The interference fringes can be read out by performing a homodyne measurement on the condensate localized in one well. We have analyzed the limitations on the accuracy of the scheme and show that a high-precision measurement can be achieved if the condensate contains a large number of coherently condensed atoms.
We consider a small F=1F=1F=1 spinor condensate inside an optical cavity driven by an optical probe field, and subject the output of the probe to a homodyne detection, with the goal of investigating the effect of measurement backaction on the spin dynamics of the condensate. Using the stochastic master equation approach, we show that the effect of backaction is sensitive to not only the measurement strength but also the quantum fluctuation of the spinor condensate. The same method is also used to estimate the atom numbers below which the effect of backaction becomes so prominent that extracting spin dynamics from this cavity-based detection scheme is no longer practical.