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arXiv:1110.3021 · Physical Review A

Phase-sensitive detection for unconventional Bose-Einstein condensation

Zi Cai, L.-M. Duan, Congjun Wu

Published Nov 2, 2012• 11 citations
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Abstract

We propose a phase-sensitive detection scheme to identify the unconventional ${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$ symmetry of the condensate wave functions of bosons, which have already been proposed and realized in high bands in optical lattices. Using the impulsive Raman operation combined with time-of-flight imaging, the off-diagonal correlation functions in momentum space give rise to the relative phase information between different components of condensate wave functions. This scheme is robust against the interaction and interband effects, and provides evidence of unconventional Bose-Einstein condensations with nontrivial condensation symmetries.

DOI
10.1103/physreva.86.051601

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We propose a phase-sensitive detection scheme to identify the unconventional px\ifmmode±\else\textpm\fiipy{p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}px​\ifmmode±\else\textpm\fiipy​ symmetry of the condensate wave functions of bosons, which have already been proposed and realized in high bands in optical lattices. Using the impulsive Raman operation combined with time-of-flight imaging, the off-diagonal correlation functions in momentum space give rise to the relative phase information between different components of condensate wave functions. This scheme is robust against the interaction and interband effects, and provides evidence of unconventional Bose-Einstein condensations with nontrivial condensation symmetries.
In the context of Gross-Pitaevskii theory, we investigate the unconventional Bose-Einstein condensations in the two-species mixture with ppp-wave symmetry in the second band of a bipartite optical lattice. An imaginary-time propagation method is developed to numerically determine the ppp-orbital condensation. Different from the single-species case, the two-species boson mixture exhibits two nonequivalent complex condensates in the intraspecies-interaction-dominating regime, exhibiting the vortex-antivortex lattice configuration in the charge and spin channels, respectively. When the interspecies interaction is tuned across the SU(2) invariant point, the system undergoes a quantum phase transition toward a checkerboardlike spin-density wave state with a real-valued condensate wave function. The influence of lattice asymmetry on the quantum phase transition is addressed. Finally, we present a phase-sensitive measurement scheme for experimentally detecting the unconventional Bose-Einstein condensation in our model.
We show that the phase of a Bose-Einstein condensate wave function of ultracold atoms in an optical lattice potential in two dimensions can be detected. The time-of-flight images, obtained in a free expansion of initially trapped atoms, are related to the initial distribution of atomic momenta but the information on the phase is lost. However, the initial atomic cloud is bounded and this information, in addition to the time-of-flight images, is sufficient in order to employ the phase retrieval algorithms. We analyze the phase retrieval methods for model wave functions in a case of a Bose-Einstein condensate in a triangular optical lattice in the presence of artificial gauge fields.
We perform a theoretical study on the recently observed unconventional Bose-Einstein condensations (UBEC) in the high bands of optical lattices. These exotic states are characterized by complex-valued condensate wave functions with nodal points or real-valued wave functions with nodal lines; thus, they are beyond the ``no-node'' theorem of conventional BECs. A quantum phase transition is driven by the competition between the single-particle band and interaction energies. The complex UBECs spontaneously break time-reversal symmetry, exhibiting a vortex-antivortex lattice structure.
We propose and demonstrate numerically a measurement scheme for complete reconstruction of the 2D quantum wave function of a Bose-Einstein condensate, amplitude and phase, from a time-of-flight measurement. We identify a fundamental ambiguity present in the measurement of phase structures of high-symmetry excitations (e.g., vortices) and show how to overcome it by allowing for different expansion durations in different directions. We demonstrate this approach with the reconstruction of matter-wave vortices and arrays of vortices.
Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms as well as condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wave function. We propose and discuss two schemes for such phase-sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for nontrivial particle-hole order parameters, such as d-density wave order.