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arXiv:0711.4007 · Physical Review Letters

Phase Separated BEC for High-Sensitivity Force Measurement

S. G. Bhongale, Eddy Timmermans

Published May 5, 2008• 17 citations
arXivHTMLPDF

Abstract

A trapped, phase separated, two component Bose-Einstein condensate (BEC) can be configured to give a single BEC bubble that floats freely in the surrounding BEC. We point out that this system gives a unique template to carry out mesoscopic quantum studies and to detect weak forces. We demonstrate the detection capabilities by proposing and studying a "quantum level" for fundamental quantum fluctuation studies and for mapping the potential energy landscape near a surface with exquisite accuracy.

DOI
10.1103/physrevlett.100.185301

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•Jan 1, 2010•0 citations
A trapped, phase separated, two component Bose-Einstein condensate (BEC) can be configured to give a single BEC bubble that floats freely in the surrounding BEC. We point out that this system gives a unique template to carry out mesoscopic quantum studies and to detect weak forces. We demonstrate the detection capabilities by proposing and studying a "quantum level" for fundamental quantum fluctuation studies and for mapping the potential energy landscape near a surface with exquisite accuracy.
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.
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).
We propose to utilize the Bose–Einstein condensate (BEC) for precision phase sensitive measurement of position and momentum displacements. The controlled two-soliton dynamics can be turned into a quantum probe to measure these parameters with high precision in an experimentally verified system of bright solitary trains. A careful phase space analysis of the dynamics of the mesoscopic wave packet is carried out through Wigner phase space picture for finding out the parameter domain exhibiting sub-Planck structures, required for precision quantum metrology. We propose two experimentally feasible scenarios, one involving the overall phase and the other through the relative phase between the two-solitons when they are oscillating inside the trap. In both the cases, detailed analytical studies are carried out through the overlap functions which reveal the sensitivity issue. A careful analysis is also performed to find the parametric domain relevant for the use of BEC for weak value estimation.
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.
In the years following the first Bose-Einstein condensation of dilute atomic gases in 1995, several experiments demonstrated many fundamental properties of two-component BEC. Subsequent to these pioneering experiments, almost a decade passed with little experimental activity, relative to investigations of single-component condensates. In somewhat of a renaissance, the initial observations of two-component BEC have been revisited in recent years, consolidating and clarifying results of the early works, and illuminating new and surprising behaviour of these rich quantum fluids. This thesis presents new experimental results on the relative phase evolution of two-component Bose-Einstein condensates (BECs). We approach our study of this system from the dual perspective of binary superfluidity and trapped atom interferometry. We observe nonequilibrium dynamics of the condensate that are deeply connected to the physics of interpenetrating superfluids. These dynamics have consequences for interferometers whose two paths are different internal spin states of the condensate atoms. Using trapped condensates for precision measurement draws upon the benefits of confined atom interferometry - long interrogation times, precise position control to measure near-field potentials - in addition to the unique coherence properties of BECs. Precision measurementwith trapped particles, however, is obstructed by the inherent inhomogeneities associated with the confinement itself. Spatial variation of the external potentials and atomic density can give rise to dephasing during the free evolution and imperfect splitting and recombination of the interferometric paths. In this thesis, we consider the dephasing of the two-componentmean field order parameter, which tends to diminish the interference signal attained with the condensate. The promise of fuhs for atom interferometry lies within using nonclassical many body states to reduce the fundamental noise limit imposed upon measuring the projection of atomic pseudospin. Before the many body quantum properties of two-component condensates can be used to their full potential, the ideal classical limit must be achieved and investigated. As in optical interferometry, the classical ideality of an interference measurement is contingent upon control of the spatialmodes - thematter wave fields, or single particle wave functions. Whilst much attention is currently focused on preparing nonclassical many body states for entanglement and squeezing of the condensate pseudospin, this thesis focuses on the ancillary yet important issue of spatial inhomogeneity of the condensate mean field. Reversal of the spatially inhomogeneous mean field evolution is demonstrated, employing the techniques of nuclear magnetic resonance. A new method is demonstrated to probe pseudospin -1/2 condensates involving microwave adiabatic passage. The technique permits simultaneous, spatially resolved absorption imaging of the spatial mode of each component. Controlled manipulation of the components into Zeeman states with different magnetic moments allows spatial separation using a Stern-Gerlach separation technique, providing a spatially resolved projection of the local condensate pseudospin from a single absorption image. We propose an interferometric technique which employs this imaging method to directly image the relative phase. The miscibility of the two components depends on the relative magnitude of the interactions between various collision partners. The boundary of this miscibility is found to be less pronounced than expected from the commonly applied results of homogeneous super-fluids.The effects of kinetic energy are shown to be significant at the threshold of miscibility, leading to a breakdown in the Thomas-Fermi approximation. Magnetic dipole transitions amongst alkali ground states are often used to prepare, manipulate, and interrogate pseudospin -1/2 condensates. We present a thorough investigation of the two-photonmagnetic dipole transitions between the |F = 1,mF = -1〉 and |F = 2,mF = +1〉 states, and the |F = 1,mF = +1〉 and |F = 2,mF = -1〉 states of 87Rb. Taking into account all 8 Zeeman levels of the electronic ground state reveals markedly different radiative shifts and effects beyond the rotating wave approximation, compared to the three-level formalism commonly used for these transitions.This has implications for Ramsey interferometry using the two-photon magnetic dipole transitions. The unchartered experimental territory offered by two-component condensates is vast, and future directions, supplementary to the work in this thesis, are elucidated.