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arXiv:cond-mat/0310053 · Physical Review A

Detecting supercounterfluidity by Ramsey spectroscopy

Anatoly B. Kuklov, Nikolay V. Prokof'ev, Boris V. Svistunov

Published Feb 26, 2004• 20 citations
arXivHTMLPDF

Abstract

A two-component system of ultracold atoms in an optical lattice at integer total filling factor and strong enough onsite repulsion can form a supercounterfluid (SCF) phase, which can be viewed as the Bose-Einstein condensate (BEC) of pairs formed by particles of one sort and holes of another sort. In this quasimolecular BEC, no single-component BEC exists, and the net atomic flow is prohibited. We show that, in the case of the interconvertible species (like hyperfine states of Rb), the corresponding order parameter can be detected by spatially selective Ramsey spectroscopy. The method can be used, in particular, for revealing a persistent supercounterflow as well as the SCF vortices---imposing a single $\ensuremath{\pi}/2$ rf-pulse will result in a specific phase-separation pattern. The detection of the SCF should be considered in conjunction with observing no typical BEC interference fringes for each component. The consequences of the strong SCF correlations persistent in the two atomic BECs phase are discussed as well.

DOI
10.1103/physreva.69.025601

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A two-component system of ultracold atoms in an optical lattice at integer total filling factor and strong enough onsite repulsion can form a supercounterfluid (SCF) phase, which can be viewed as the Bose-Einstein condensate (BEC) of pairs formed by particles of one sort and holes of another sort. In this quasimolecular BEC, no single-component BEC exists, and the net atomic flow is prohibited. We show that, in the case of the interconvertible species (like hyperfine states of Rb), the corresponding order parameter can be detected by spatially selective Ramsey spectroscopy. The method can be used, in particular, for revealing a persistent supercounterflow as well as the SCF vortices---imposing a single \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 rf-pulse will result in a specific phase-separation pattern. The detection of the SCF should be considered in conjunction with observing no typical BEC interference fringes for each component. The consequences of the strong SCF correlations persistent in the two atomic BECs phase are discussed as well.
Ramsey interferometry as one of the most important high-precision measurement methods has prospects for inferring various properties of ultracold atoms and molecules. We investigate the multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate (BEC) in an optical cavity. Compared with the standard two-pulse Ramsey scheme, our multi-pulse Ramsey proposal greatly relaxes the requirements for both intensity and width of the pulses, allowing the interferometry to be achieved using weak and narrow pulses. When the pumping pulses characterizing the coupling between the cavity field and the atomic BEC are applied to the zero background field, we demonstrate the atomic Ramsey fringes in the time domain for different pulse numbers and different pulse widths. We find that although the multi-pulse Ramsey fringes are no longer sensitive to cavity-pump detuning, they can still record the information of the interaction between coherent atoms. We obtain the fundamental frequency of the multi-pulse Ramsey fringes analytically and find that it is proportional to the number of pulses. Particularly, it is shown that the minimum of the fundamental frequency is exactly the critical point of the phase transition of the system. For a nonzero background field, the results indicate that a nondestructive observation of atomic Ramsey fringes by cavity transmission spectroscopy is feasible. Our findings provide insights for improving the accuracy of Ramsey interferometry and for using interferometry to observe phase transitions.
We study the supercounterfluid (SCF) states in the two-component hard-core Bose-Hubbard model on a square lattice, using the quantum Monte Carlo method based on the worm (directed-loop) algorithm. Since the SCF state is a state of a pair condensation characterized by $\ensuremath{\langle}{a}^{\ifmmode\dagger\else\textdagger\fi{}}b\ensuremath{\rangle}\ensuremath{\ne}0,\ensuremath{\langle}a\ensuremath{\rangle}=0$, and $\ensuremath{\langle}b\ensuremath{\rangle}=0$, where aaa and bbb are the order parameters of the two components, it is important to study behaviors of the pair-correlation function $\ensuremath{\langle}{a}_{i}{b}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}{b}_{j}\ensuremath{\rangle}$. For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair correlation, we confirm the Kosterlitz-Thouless character of the SCF phase. The simulation efficiency is also improved in the SCF phase.
Depending on the Hamiltonian parameters, two-component bosons in an optical lattice can form at least three different superfluid phases in which both components participate in the superflow: a (strongly interacting) mixture of two miscible superfluids (2SF), a paired superfluid (PSF) vacuum, and (at a commensurate total filling factor) the super-counter-fluid (SCF) state. We study the universal properties of the 2SF-PSF and 2SF-SCF quantum phase transitions and show that (i) they can be mapped onto each other and (ii) their universality class is identical to the (d+1)-dimensional normal-superfluid transition in a single-component liquid. The finite-temperature 2SF-PSF(SCF) transitions and the topological properties of 2SF-PSF(SCF) interfaces are also discussed.
Ultracold atoms and Bose-Einstein condensates represent a burgeoning and ever exciting area of research which has produced numerous breakthroughs in the last 15 years. Ultracold atoms at nano-Kelvin temperatures, isolated in atom traps from the hot, room temperature environment, exhibit ultimate quantum properties and can serve as pure samples for testing quantum mechanics and performing precision measurements. The research described in this thesis investigates, both theoretically and experimentally, the coherence and dynamical evolution of a two-component Bose-Einstein condensate (BEC). The studies are performed on the |1 › ≡ F = 1,mF = −1 › and |2 › ≡ |F = 2,mF = +1 › hyperfine ground states of a 87Rb BEC trapped on an atom chip. Conventional understanding has been that the fringe contrast in interferometric experiments on a BEC is limited by the mean-field dephasing due to strong interatomic interactions which lead to inhomogeneous collisional shifts. We have discovered using Ramsey interferometry a mean-field driven self-rephasing effect in a trapped twocomponent BEC. When combined with a spin-echo technique, we find that the selfrephasing leads to a coherence time of 2.8 s, the longest ever recorded for an interacting BEC. Secondly, we have developed a new technique based on periodic collective oscillations for precision measurements of the interspecies and intraspecies scattering lengths and derived an analytic mean-field theory for the phase and density dynamics in the twocomponent BEC. This technique has been applied to the measurements of the scattering lengths for the two components, |1i and |2i, in 87Rb with a precision of 0.016%. Additionally, the two-body loss coefficients for these states have been measured. Thirdly, we have developed and applied a new, interferometric method for calibrating the detection system, in order to determine the total atom number precisely for Ramsey interferometric measurements. The calibration coefficient is found to be in a good agreement with that obtained using a conventional calibration technique based on the critical BEC temperature. Finally, we have detected predicted RF-induced Feshbach resonances by monitoring changes in the two-body loss coefficients in the two-component BEC. Conventional Feshbach resonances have been used in many works to tune the s-wave interactions; however, there is no achievable magnetic Feshbach resonance for magnetically trappable states of 87Rb. The RF-induced resonances which we have detected can provide a way to tune the scattering lengths which is important for interferometry and entanglement experiments. The positions of the resonances may provide useful information for predicting the atomic scattering properties of 87Rb.
Taking Rosen-Zener tunneling as the underlying process，a scheme to achieve nonlinear Ramsey interferometry with a two-component trapped Bose-Einstein condensate is proposed. Abundant nonlinear Ramsey interference fringes are observed in time domain by the numerical simulations and these fringes are very different from the sinusoidal pattern for linear Ramsey interference due to the dominant nonlinear interaction between atoms. Furthermore，Fourier transformation results show that the fundamental frequency of Ramsey fringes can exactly reflect the information of nonlinearity or asymmetry. This finding provides an opportunity to measure atomic properties via measuring the frequency of fringes.
We propose a feasible scheme to realize nonlinear Ramsey interferometry with a two-component Bose-Einstein condensate, where the nonlinearity arises from the interaction between coherent atoms. In our scheme, two Rosen-Zener pulses are separated by an intermediate holding period of variable duration and through varying the holding period we have observed nice Ramsey interference patterns in the time domain. In contrast to the standard Ramsey fringes our nonlinear Ramsey patterns display diversiform structures ascribed to the interplay of the nonlinearity and asymmetry. In particular, we find that the frequency of the nonlinear Ramsey fringes exactly reflects the strength of nonlinearity as well as the asymmetry of system. Our finding suggests a potential application of the nonlinear Ramsey interferometry in calibrating the atomic parameters such as scattering length and energy spectrum.