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Quantum Electronics and Laser Science Conference

Weak force detection using a Bose-Einstein condensate

Joel Frederick Corney, Gerard J Milburn, Weiping Zhang

Published Jan 20, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.1999.807142

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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 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.
We investigate the possibility of detecting a weak coherent force by means of a hybrid optomechanical quantum device formed by a Bose Einstein Condensate (BEC) confined in a high quality factor optical cavity with an oscillatory end mirror. We show using the stochastic cooling technique that the atomic two-body interaction can be utilized to cool the mirror and achieve position squeezing essential for making sensitive measurements of weak forces. We further show that the atomic two-body interaction can also increase the signal to noise ratio (SNR) and decrease the noise of the off-resonant stationary spectral measurements.
This thesis considers measurements that could be used to verify the existence of a coherent superposition, using the specific example of a superposition of a Bose-Einstein condensate in a double-well. There is significant interest in superposition states in atomic condensates, due to the possibility of large numbers of atoms being involved in the superposition, and while various experimental proposals exist for generating such states none have yet been successfully verified in this system. We use a number-state description of the condensate in a double well, which is a number-conserving approach with basis states specifying the number of atoms in each well. This allows us to consider 'NOON`-type states, i.e. a superposition of the 'N,0' state of all atoms localized in the left well and the '0,N' state where all N atoms are localized in the right hand well. MATLAB is used to solve for the ground state, dynamics, and measurement expectation values for the double-well condensate in this basis. We consider measurements that would distinguish this coherent superposition from a statistical mixture of the same states. Such a suitable measurement is the parity of the atoms in one well, after a Ramsey-type interference experiment has been performed. We have found that unambiguously distinguishing even a perfect 'NOON' state from a statistical mixture using standard detection methods will present experimental difficulties. We find that interactions between condensate atoms degrade the visibility of the parity oscillations, and we also consider the effects of detector inefficiency on these parity measurements. We suggest that a 'NOON'-type superposition state in the double-well system could be generated in a reasonable time frame by making use of a Feshbach resonance to tune the inter-atomic interactions from repulsive to negative. We find that even with imperfect superpositions, parity measurements retain their frequency dependence, which is the signature of NOON-type coherence.
We investigate the possibility of cooling a mechanical oscillator to its ground state and using it to detect a weak coherent force by means of a hybrid optomechanical quantum device formed by a Bose-Einstein condensate (BEC) confined in a high quality factor optical cavity with an oscillatory end mirror. We show using the stochastic cooling technique that the atomic two-body interaction can be utilized to cool the mirror and achieve position squeezing essential for making sensitive measurements of weak forces. We further show that for certain values of the system parameters and spectral range, the atomic two-body interaction can also increase the signal-to-noise ratio and decrease the noise of the off-resonant stationary spectral measurements. We show that the minimum noise is obtained only in the presence of BEC.