Quantum simulation of competing orders with fermions in quantum optical lattices

Abstract

Ultracold Fermi atoms confined in optical lattices coupled to quantized modes of an optical cavity are an ideal scenario to engineer quantum simulators in the strongly interacting regime. The system has both short range and cavity induced long range interactions. We propose such a scheme to investigate the coexistence of superfluid pairing, density order and quantum domains having antiferromagnetic or density order in the Hubbard model in a high finesse optical cavity at T = 0. We demonstrate that those phases can be accessed by properly tuning the linear polarizer of an external pump beam via the cavity back-action effect, while modulating the system doping. This allows emulate the typical scenarios of analog strongly correlated electronic systems.Introduction. Coupling ultracold quantum gases to high-finesse optical cavities is a novel scenario to explore many-body phases in the full quantum regime by exploiting the controllability of light-matter interaction [1,2]. Major experimental breakthroughs have been achieved in the quantum limit of both light and matter. For instance, the Dicke phase transition has been observed in a Bose-Einstein condensate coupled to cavity modes [3]. Experimentally, it has been achieved the emergence and control of supersolid phases where the cavity backaction generates light-induced effective long-range interactions which compete with short-range interatomic interactions [4][5][6][7][8].On the theoretical side, recent studies have introduced settings where cavity fields generate gauge-fields [9, 10], artificial spin-orbit coupling [11], self-organized phases [12,13], topological phases [14,15], measurement induced entangled modes [16], induced magnetic and density order using measurement back action [17] and feedback control [18], dimerization [19], spin lattice systems [20] and quantum simulators based on global collective lightmatter interactions [21,22].

Cavityless self-organization of ultracold atoms due to the feedback-induced phase transition

“…In particular, one can measure light scattered at an angle that does not satisfy the condition (1), which would contain different information about the distribution of the atoms [58][59][60][61] . The feedback-induced maximization of this signal might result in more exotic states of the atomic ensembles, both bosons and fermions 28,29,[62][63][64][65][66][67][68][69][70] . We leave this interesting possibility for future research.…”

Cavity-Mediated Unconventional Pairing in Ultracold Fermionic Atoms

“…Artificial magnetic fields can be induced to create distinct topological phases [27][28][29]. Most importantly, various types of cavity-mediated interactions could give rise to a plethora of many-body phases [30][31][32][33][34][35][36][37][38], including superfluid and charge density states, and even more exotic phases with no direct analog in condensed matter systems. All these developments render ultracold fermionic atoms natural candidates to explore exotic physics, such as topological phases [39][40][41], which would be more difficult to observe in condensed matter.…”

“…The lattice is placed into a cavity setup sketched in Fig. 1, where two cavities oriented along the optical lattice axes induce atomic interactions as described theoretically in detail, e.g., in [35].…”

“…As a consequence, the interaction can mediate pairing of both singlet and triplet pairs. Previous theoretical works describing cavity-mediated interactions of fermionic atoms had focused on one-dimensional lattices [33][34][35][36]. In [36], the spin states were energetically separated, such that the cavity coupling was shown to induce either singlet superfluidity or spin-density order.…”

“…Here, we focus instead on a regime with | k c | π, where we show that different superfluid instabilities compete. This regime could be realised either by employing an infrared or a terahertz cavity, or by tilting the axis of an optical cavity with respect to the atomic gas, such that only the cavity wavevector's projection onto the gas plane is transferred to the atoms [35]. In this regime, there is no nesting of wavevectors, and competing density wave instabilities are suppressed.…”