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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Detection of macroscopic quantum coherence of a Bose-Einstein condensate by electronic spin echo

Weiping Zhang, Guoqiang Liu

Published May 1, 1997• 1 citation
Publisher

Abstract

In this paper the conventional electronic spin echo technique is proposed to detect the macroscopic quantum coherence of a Bose-Einstein condensate. In this technique, a (pi) /2 microwave pulse followed by a (pi) pulse with an appropriate delay is used to excite the Zeeman levels of a Bose condensed gas. After the two pulses, a spin echo pulse is generated due to the dephasing and rephasing processes in the gas. We show that the properties of the spin echo signal depends on the temperature of the gas. If a condensate exists in the gas, the echo signal can reflect the macroscopic quantum coherence of the Bose-Einstein condensate. The detection technique doesn't destroy the sample.

DOI
10.1117/12.273763

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In this paper the conventional electronic spin echo technique is proposed to detect the macroscopic quantum coherence of a Bose-Einstein condensate. In this technique, a (pi) /2 microwave pulse followed by a (pi) pulse with an appropriate delay is used to excite the Zeeman levels of a Bose condensed gas. After the two pulses, a spin echo pulse is generated due to the dephasing and rephasing processes in the gas. We show that the properties of the spin echo signal depends on the temperature of the gas. If a condensate exists in the gas, the echo signal can reflect the macroscopic quantum coherence of the Bose-Einstein condensate. The detection technique doesn't destroy the sample.
Study of the physical properties of Bose condensed gases has recently become a very active topic due to the experimental realizations of Bose-Einstein condensation in magnetically trapped gases of alkali atoms. In this paper we theoretically study the microwave electronic spin resonance of a weakly interacting Bose gas. For a Bose gas above the critical temperature for Bose-Einstein condensation, the microwave radiation induced by the driving microwave field in the electronic spin resonance exhibits the ordinary Rabi oscillation damped by the inhomogeneous Doppler dephasing. For a Bose gas with a condensate, the induced radiation is composed of two components. One is the strong coherent Rabi oscillation from the condensate. The other is a modulated Rabi oscillation due to the noncondensed part of the gas. We show that the modulation of Rabi oscillation of the noncondensed gas is directly related to the elementary collective excitation of atoms in the gas.
We simulate the effect of special excitation pulses on a cold gas of atoms. First, a rotary echo sequence is used to examine the coherent nature of a frozen Rydberg gas. If collective excitation and de-excitation is present with little or no source of dephasing, after these pulses the system should be returned to a state with few excitations, and a strong echo signal should occur. We investigate systems that should display a perfect echo and systems where the interaction between atoms reduces the echo signal. A spin echo sequence is also used on a system of coherent hopping excitations, and we simulate how the strength of a spin echo signal is affected by thermal motion.
The development of ultracold atom technology has enabled precise investigations on the quantum dynamics of quantum gases. Recently, inspired by experimental advancement, the SU(1,1)\text{SU}(1,1)SU(1,1) echo, akin to the well-known SU(2)\text{SU}(2)SU(2) spin echo, was proposed for the single-component Bose-Einstein condensate (BEC). In this paper, we investigate the possibility of quantum echo in the more intricate two-component BEC by fully exploiting its underlying symmetry, which is the Lie group Sp(4,R)\text{Sp}(4,R)Sp(4,R). We demonstrate that quantum echo can occur for the two-component BEC by applying a driving protocol consisting of two steps in each period. The first step can be any Bogoliubov Hamiltonian, while the second step is a Hamiltonian with interactions turned off, which plays a similar role as the $\ensuremath{\pi}$ pulse in spin echo. We confirm our theoretical results with numerical calculations for different examples of the two-component BEC. We further consider the effect of interactions between the excited boson modes on the quantum echo process and discuss the possible experimental implementation of this quantum echo.
The study of physical properties of Bose condensed gases has recently become a very active topic due to the experimental realization of Bose-Einstein condensation in the magnetically trapped gases of alkali atoms. In this paper we theoretically study the Rabi oscillation of a weakly interacting Bose gas in the regime of microwave electronic spin resonance. For a Bose gas above the critical temperature for Bose-Einstein condensation, the microwave radiation induced by the driving microwave field exhibits the ordinary Rabi oscillation damped by the inhomogeneous Doppler dephasing. For a Bose gas with a condensate, the microwave radiation is composed of two components. One is the strong coherent Rabi oscillation from the condensate. The other is a modulated Rabi oscillation due to the noncondensed part of the gas. We show that the modulation of Rabi oscillation of the noncondensed gas is directly relative to the elementary collective excitation of atoms in the gas.
There has been much recent interest in the use of optical photon echoes for information storage and processing. Unfortunately, existing optical echo memories require doped crystals at liquid He temperature. The proposed scheme uses an optically excited microwave spin echo to store optical temporal information in the Raman excited ground state coherences. The advantage is that microwave echoes are known to exist at room temperature with decay times approaching 1 s in certain materials. We show that these spin echoes can be excited and detected optically, thereby allowing storage densities that are comparable to the optical echo techniques. Briefly, a three level A system is used, which can be excited by two near resonant optical transitions or one near resonant microwave transition. The Raman interaction first stores temporal and phase information in an inhomogeneously broadened ground states coherence. A microwave π-pulse is used to time-reverse the coherences, thus generating spin echoes that can be detected optically by a Raman probe. Preliminary experimental results will also be reviewed.
We report the realization of a Bose-Einstein condensate of metastable atoms (helium in the lowest triplet state). The excitation energy of each atom with respect to the ground state is 20 electron volts, but inelastic processes that would destroy the sample are suppressed strongly enough in a spin-polarized sample to allow condensation. Our detection scheme takes advantage of the metastability to achieve detection of individual atoms as well as of the decay products of inelastic processes. This detection opens the way toward new studies in mesoscopic quantum statistical physics, as well as in atomic quantum optics.