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arXiv:1809.09884 · Physical Review A

Cavity-induced superconducting and 4kF charge-density-wave states

Ameneh Sheikhan, Corinna Kollath

Published May 21, 2019• 20 citations
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Abstract

We propose two experimental setups for fermionic atoms in a high-finesse optical resonator in which either a superconducting state with $s$-wave symmetry of the pairs or a $4{k}_{F}$ charge-density wave can self-organize. In order to stabilize the $s$-wave pairing, a two component attractively interacting fermionic gas is confined to a one-dimensional chain structure by an optical lattice. The tunneling of the atoms along the chains is suppressed initially by an energy offset between neighboring sites. A Raman transition using the cavity mode and a transversal pump laser then reintroduces a cavity-assisted tunneling. The feedback mechanism between the cavity field and the atoms leads to a spontaneous occupation of the cavity field and of a state of the fermionic atoms which is dominated by $s$-wave pairing correlations. Extending the setup to a quasi-one-dimensional ladder structure where the tunneling of atoms along the rungs of the ladder is cavity assisted, the repulsively interacting fermionic atoms self-organize into a $4{k}_{F}$ charge-density wave. We use adiabatic elimination of the cavity field combined with state-of-the-art density-matrix renormalization-group methods in finite systems in order to identify the steady-state phases of the system.

DOI
10.1103/physreva.99.053611

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We propose two experimental setups for fermionic atoms in a high-finesse optical resonator in which either a superconducting state with sss-wave symmetry of the pairs or a 4kF4{k}_{F}4kF​ charge-density wave can self-organize. In order to stabilize the sss-wave pairing, a two component attractively interacting fermionic gas is confined to a one-dimensional chain structure by an optical lattice. The tunneling of the atoms along the chains is suppressed initially by an energy offset between neighboring sites. A Raman transition using the cavity mode and a transversal pump laser then reintroduces a cavity-assisted tunneling. The feedback mechanism between the cavity field and the atoms leads to a spontaneous occupation of the cavity field and of a state of the fermionic atoms which is dominated by sss-wave pairing correlations. Extending the setup to a quasi-one-dimensional ladder structure where the tunneling of atoms along the rungs of the ladder is cavity assisted, the repulsively interacting fermionic atoms self-organize into a 4kF4{k}_{F}4kF​ charge-density wave. We use adiabatic elimination of the cavity field combined with state-of-the-art density-matrix renormalization-group methods in finite systems in order to identify the steady-state phases of the system.
We consider theoretically ultracold interacting bosonic atoms confined to quasi-one-dimensional ladder structures formed by optical lattices and coupled to the field of an optical cavity. The atoms can collect a spatial phase imprint during a cavity-assisted tunneling along a rung via Raman transitions employing a cavity mode and a transverse running wave pump beam. By adiabatic elimination of the cavity field we obtain an effective Hamiltonian for the bosonic atoms, with a self-consistency condition. Using the numerical density-matrix renormalization-group method, we obtain a rich steady-state diagram of self-organized steady states. Transitions between superfluid to Mott-insulating states occur, on top of which we can have Meissner, vortex liquid, and vortex lattice phases. Also a state that explicitly breaks the symmetry between the two legs of the ladder, namely, the biased-ladder phase, is dynamically stabilized. We investigate the influence that a trapping potential has on the stability of the self-organized phases.
We investigate ultracold fermions placed into an optical cavity and subjected to optical lattices which confine the atoms to ladder structures. A transverse running-wave laser beam induces together with the dynamical cavity field a two-photon Raman-assisted tunneling process with spatially dependent phase imprint along the rungs of the ladders. We identify the steady states which can occur by the feedback mechanism between the cavity field and the atoms. We find the spontaneous emergence of a finite cavity field amplitude which leads to an artificial magnetic field felt by the fermionic atoms. These form a chiral insulating or chiral liquid state carrying a chiral current. We explore the rich state diagram as a function of the power of the transverse laser beam, the atomic filling, and the phase imprint during the cavity-induced tunneling. Both a sudden onset or a slow exponential activation with the transverse laser power of the self-organized chiral states can occur.
Recent quantum gas cavity-QED experiments demonstrated simultaneous coupling of photons to single atom transitions as well as correlated pairs of ultracold fermions trapped inside optical cavities. This enables simultaneous control over density ordering and pairing. Using extensive numerical simulations, we show that in a transversely driven, two-component degenerate Fermi gas, the interplay of cavity-induced and bare atom--atom interactions controls not only the power threshold for self-organization, but also the type of spatial ordering in the Z2\mathbb Z_2Z2​-symmetry-broken superradiant state. In the repulsive interaction regime, unpaired or weakly paired fermions first self-organize through a charge-density-wave instability, and finite-momentum pairing only occurs at much stronger pump strengths. In contrast, an attractive superfluid undergoes a joint density--pairing instability, directly entering into intertwined phase with charge-density-wave and pair-density-wave orders. At strong pumping the photon-enhanced pair interaction generates localized density and pairing order even when the bare contact interaction is repulsive. In this cavity-dominated regime strong spatial localization suppresses the long range superfluid coherence. Our results identify the role of cavity-induced atomic interactions in supporting intertwined fermionic orders and pave the way for exploring exotic states with multiple orders in highly controlled hybrid light-matter systems.
We investigate fermionic atoms subjected to an optical lattice and coupled to a high finesse optical cavity with photon losses. A transverse pump beam introduces a coupling between the atoms and the cavity field. We explore the steady-state phase diagram taking fluctuations around the mean field of the atoms-cavity coupling into account. Our approach allows us to investigate both one- and higher-dimensional atomic systems. The fluctuations beyond mean field lead to an effective temperature that changes the nature of the self-organization transition. We find a strong dependence of the results on the atomic filling, in particular when contrasting the behavior at low filling and at half filling. At low filling, the transition to a self-organized phase takes place at a critical value of the pump strength. In the self-organized phase, the cavity field takes a finite expectation value and the atoms show a modulation in the density. Surprisingly, at even larger pump strengths a strongly nonmonotonous behavior of the temperature is found and hints toward effects of cavity cooling at many-body resonances. Additionally multiple self-organized stable solutions of the cavity field and the atoms occur, signaling the presence of a fluctuation-induced bistability, with the two solutions having different effective temperatures previously discussed by Tolle . []. In contrast, at half filling a bistable region arises at the self-organization transition already neglecting the fluctuations. The presence of the fluctuations induce an effective temperature, as at lower fillings, and change the behavior of the transition and the steady states drastically. We analyze the properties of the occurring steady states of the coupled atoms-cavity system.
We explore the density and spin self-ordering of driven spin-1/2 collisionless fermionic atoms coupled to the electromagnetic fields of a ring resonator. The two spin states are two-photon Raman-coupled via a pair of degenerate counterpropagating cavity modes and two transverse pump fields. In this one-dimensional configuration the coupled atom-field system possesses a continuous U (1) translational symmetry and a discrete Z 2 spin inversion symmetry. At half filling for sufficiently strong pump strengths, the combined U (1) × Z 2 symmetry is spontaneously broken at the onset of a superradiant phase transition to a state with self-ordered density and spin structures. We predominately find an antiferromagnetic lattice order at the cavity wavelength. The self-ordered states exhibit unexpected positive momentum pair correlations between fermions with opposite spin. These strong cavity-mediated correlations vanish at higher pump strength.
We propose how topologically nontrivial states can dynamically organize in a fermionic quantum gas that is confined to a two-dimensional optical lattice potential and coupled to the field of an optical cavity. The spontaneously emerging cavity field induces, together with coherent pump laser fields, a dynamical gauge field for the atoms. Upon adiabatic elimination of the cavity degree of freedom, the system is described by an effective Hofstadter model with a self-consistency condition that determines the tunneling amplitude along the cavity direction. The fermions are found to self-organize into topologically nontrivial states that carry an extended edge state for a finite system size. Due to the dissipative nature of the cavity field, the topological steady states are protected from external perturbations.