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arXiv:0906.0931

Detecting d-wave superfluid and d-density wave states of ultracold Fermions on optical lattices

David Pekker, Rajdeep Sensarma, Eugene Demler

Published Jun 4, 2009• 0 citations
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Abstract

We propose a pump probe experiment for detecting the d-wave superfluid and d-density wave phases of ultracold Fermions on an optical lattice. The pump consists of periodic modulations of the optical lattice intensity which creates quasiparticle pairs in these systems. The changes in the momentum distribution under the drive can be used to measure quasiparticle dispersion and gap anisotropy. Further, we show that the pattern of peaks and dips in the spin selective density-density correlation function provides a phase sensitive probe of the symmetry of the order parameter in these systems.

DOI
10.48550/arxiv.0906.0931

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We propose a pump probe experiment for detecting the d-wave superfluid and d-density wave phases of ultracold Fermions on an optical lattice. The pump consists of periodic modulations of the optical lattice intensity which creates quasiparticle pairs in these systems. The changes in the momentum distribution under the drive can be used to measure quasiparticle dispersion and gap anisotropy. Further, we show that the pattern of peaks and dips in the spin selective density-density correlation function provides a phase sensitive probe of the symmetry of the order parameter in these systems.
We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time-dependent density-matrix renormalization-group method that the position of the peak in the spectrum of the induced double occupancy gives the pairing energy in a superfluid and the interaction energy in a Mott insulator, respectively. In the Mott insulator we relate the spectral weight of the peak to the spin ordering at finite temperature using perturbative calculations.
We examine antiferromagnetic and ddd-wave superfluid phases of cold fermionic atoms with repulsive interactions in a two-dimensional optical lattice combined with a harmonic trapping potential. For experimentally realistic parameters, the trapping potential leads to the coexistence of magnetic and superfluid ordered phases with the normal phase. We study the intriguing shell structures arising from the competition between the magnetic and superfluid order as a function of the filling fraction. In certain cases, antiferromagnetism induces superfluidity by charge redistributions. We furthermore demonstrate how these shell structures can be detected as distinct antibunching dips and pairing peaks in the density-density correlation function probed in expansion experiments.
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.
We propose an experimental protocol to study ppp-wave superfluidity in a spin-polarized cold Fermi gas tuned by an sss-wave Feshbach resonance. A crucial ingredient is to add a quasi-one-dimensional optical lattice and tune the fillings of two spins to the sss and ppp band, respectively. The pairing order parameter is confirmed to inherit ppp-wave symmetry in its center-of-mass motion. We find that it can further develop into a state of unexpected $\ensuremath{\pi}$-phase modulation in a broad parameter regime. Experimental signatures are predicted in the momentum distributions, density of states, and spatial densities for a realistic experimental setup with a shallow trap. The $\ensuremath{\pi}$-phase ppp-wave superfluid is reminiscent of the $\ensuremath{\pi}$ state in superconductor-ferromagnet heterostructures but differs in symmetry and physical origin. The spatially varying phases of the superfluid gap provide an approach to synthetic magnetic fields for neutral atoms. It would represent another example of ppp-wave pairing, first discovered in 3He^{3}\mathrm{He}3He liquids.
We propose an all-optical scheme to probe the dynamical correlations of a strongly interacting gas of ultracold atoms in an optical lattice potential. The proposed technique is based on a pump-and-probe scheme: a coherent light pulse is initially converted into an atomic coherence and later retrieved after a variable storage time. The efficiency of the proposed method to measure the two-time one-particle Green function of the gas is validated by numerical and analytical calculations of the expected signal for the two cases of a normal Fermi gas and a BCS superfluid state. Protocols to extract the superfluid gap and the full quasiparticle dispersions are discussed.
We propose an all-optical scheme to probe the dynamical correlations of a strongly interacting gas of ultracold atoms in an optical lattice potential. The proposed technique is based on a pump-and-probe scheme: a coherent light pulse is initially converted into an atomic coherence and later retrieved after a variable storage time. The efficiency of the proposed method to measure the two-time one-particle Green function of the gas is validated by numerical and analytical calculations of the expected signal for the two cases of a normal Fermi gas and a BCS superfluid state. Protocols to extract the superfluid gap and the full quasiparticle dispersions are discussed.