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arXiv:cond-mat/0603561

Time evolution and matter wave interference in Fermi condensates

Wei Zhang, C. A. R. Sá de Melo

Published Mar 21, 2006• 0 citations
arXivHTMLPDF

Abstract

We discuss matter wave interference of Fermi condensates in strongly coupled s-wave and p-wave channels and the time evolution of a single cloud upon release from trap. In s-wave systems, where the order parameter is a complex scalar, we find that the interference patterns depend on the relative phase of the order parameters of the condensates. In p-wave systems involving the mixture of two-hyperfine states, we show that the interference pattern exhibits a polarization effect depending on the relative orientation of the two vector order parameters. However, in p-wave systems involving a single hyperfine state, we show that this angular effect reduces to an overall phase difference between the two interfering clouds, similar to s-wave. Lastly, we also point out that p-wave Fermi condensates exhibit an anisotropic expansion, reflecting the spatial anisotropy of the underlying interaction between fermions and the orbital nature of the vector order parameter.

DOI
10.48550/arxiv.cond-mat/0603561

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We discuss matter wave interference of Fermi condensates in strongly coupled s-wave and p-wave channels and the time evolution of a single cloud upon release from trap. In s-wave systems, where the order parameter is a complex scalar, we find that the interference patterns depend on the relative phase of the order parameters of the condensates. In p-wave systems involving the mixture of two-hyperfine states, we show that the interference pattern exhibits a polarization effect depending on the relative orientation of the two vector order parameters. However, in p-wave systems involving a single hyperfine state, we show that this angular effect reduces to an overall phase difference between the two interfering clouds, similar to s-wave. Lastly, we also point out that p-wave Fermi condensates exhibit an anisotropic expansion, reflecting the spatial anisotropy of the underlying interaction between fermions and the orbital nature of the vector order parameter.
We discuss the time evolution and matter-wave interference of Fermi condensates on the Bose-Einstein condensate side of Feshbach resonances for sss- and ppp-wave superfluids, upon release from harmonic traps. In sss-wave systems, where the order parameter is a complex scalar, we find that the interference patterns depend on the relative phase of the order parameters of the condensates. In ppp-wave systems involving the mixture of two hyperfine states, we show that the interference pattern exhibits a polarization effect depending on the relative orientation of the two vector order parameters. Lastly, we also point out that ppp-wave Fermi condensates exhibit an anisotropic expansion, reflecting the spatial anisotropy of the underlying interaction between fermions and the orbital nature of the vector order parameter. Potential applications of our results include systems of ultracold atoms that exhibit ppp-wave Feshbach resonances, such as 6Li^{6}\mathrm{Li}6Li or 40K^{40}\mathrm{K}40K.
We discuss the time-of-flight expansion of dilute p-wave Fermi condensates on the BEC side of Feshbach resonances, as a way to extract information about the order parameter symmetry for superfluidity. We show that the cloud profile is in general sensitive to the interaction strength between fermions, the magnitude and direction of external magnetic fields, and to the angular momentum projection of the order parameter. In particular, due to the anisotropic nature of p-wave interactions we show that the time-of-flight expansion of a p-wave superfluid is anisotropic even if the superfluid is confined to a completely isotropic trap, unlike the case of Bose or s-wave Fermi condensates, which under the same circumstances expand isotropically. Furthermore, we demonstrate that expanding p-wave superfluids released from axially symmetric traps experience anisotropy inversions, where the aspect ratio between the axial and radial directions change during expansion, while the axial symmetry can also be lost reflecting the spatial anisotropy of the underlying interaction.
This thesis presents theoretical investigations of triplet superfluidity (triplet superconductivity) in quasi-one-dimensional organic conductors and ultra-cold Fermi gases. Triplet superfluidity is different from its s-wave singlet counterpart since the order parameter is a complex vector and the interaction between fermions is in general anisotropic. Because of these distinctions, triplet superfluids have different physical properties in comparison to the s-wave case. The author discusses in this thesis the interplay between triplet superconductivity and spin density waves in quasi-one-dimensional organic conductors, and proposes a coexistence region of the two orders. Within the coexistence region, the interaction between the two order parameters acquires a vector structure, and induces an anomalous magnetic field effect. Furthermore, the author analyzes the matter-wave interference between two p-wave Fermi condensates, and proposes a polarization effect. For a single harmonically trapped p-wave Fermi condensate, the author also shows that the expansion upon release from the trap can be anisotropic, which reflects the anisotropy of the p-wave interaction.
Abstract In quantum mechanics, each particle is described by a complex valued wave-function characterized by amplitude and phase. When many particles interact each other, cooperative phenomena give rise to a quantum many-body state with a specific quantum coherence. What is the interplay between single-particle’s phase coherence and many-body quantum coherence? Over the years, such question has been object of profound analysis in quantum physics. Here, we demonstrate how the time-dependent interference formed by releasing an interacting degenerate Fermi gas from a specific matter-wave circuit in an effective magnetic field can tell apart the two notions. Single-particle phase coherence, indicated by the first-order correlator, and many-body quantum coherence, indicated by the density–density correlator, are displayed as distinct features of the interferogram. Single particle phase coherence produces spiral interference of the Fermi orbitals at intermediate times. Many-body quantum coherence emerges as long times interference. The interplay between single-particle coherence and many-body coherence is reflected in a stepwise dependence of the interference pattern on the effective magnetic field.
For a Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattice, using the mean-field Gross–Pitaevskii (G-P) equation and the propagator method, we obtain the analytical result of the order parameter for matter wave interference at any time. The evolution of the interference pattern under a variation of the relative phase Δϕ between successive subcondensates trapped on an optical lattices is also studied. For Δϕ = π, the interference pattern is symmetric with two sharp peaks, which are symmetrically located on a straight line on both sides of a vacant central peak and moving apart from each other. This work is in agreement with available experimental results.
In quantum mechanics, each particle is described by a complex valued wave function characterized by amplitude and phase. When many particles interact each other, cooperative phenomena give rise to a quantum many-body state with a specific quantum coherence. What is the interplay between particle's phase coherence and many-body quantum coherence? Over the years, such question has been object of profound analysis in quantum physics. Here, we demonstrate how state of the art quantum technology allows to explore the question operatively. To this end, we study the time-dependent interference formed by releasing an interacting degenerate Fermi-gas from a specific matter-wave circuit in an effective magnetic field. Particle phase coherence, indicated by the first-order correlator, and many-body quantum coherence, indicated by the noise correlator, are displayed as distinct features of the interferogram. Particle phase coherence produces spiral interference of the Fermi orbitals at intermediate times. Many-body quantum coherence emerges at long times. The coupling between particles coherence and many-body coherence is reflected in a specific dependence of the interference pattern on the effective magnetic field.