Formation of Feshbach molecules in the presence of artificial spin-orbit coupling and Zeeman fields

Abstract

We derive general conditions for the emergence of singlet Feshbach molecules in the presence of artificial Zeeman fields for arbritary mixtures of Rashba and Dresselhaus spin-orbit orbit coupling in two or three dimensions. We focus on the formation of two-particle bound states resulting from interactions between ultra-cold spin-1/2 fermions, under the assumption that interactions are shortranged and occur only in the s-wave channel. In this case, we calculate explicitly binding energies of Feshbach molecules and analyze their dependence on spin-orbit couplings, Zeeman fields, interactions and center of mass momentum, paying particular attention to the experimentally relevant case of spin-orbit couplings with equal Rashba and Dresselhaus (ERD) amplitudes. The effects of spin-orbit interactions is ubiquitous in nature, from the macroscopic scale of the Earth-Moon complex in astronomy and astrophysics, to the microscopic scale of the electron in the hydrogen atom in atomic physics. The interest in spin-orbit coupled systems has been revived in condensed matter physics due the emergence of non-trivial topological properties of insulators and superconductors subject to Rashba spinorbit fields [1,2], and in atomic physics due to the creation of artificial spin-orbit coupling in ultra-cold atoms [3], which made possible the study of special quantum phase transitions in bosonic systems.This new tool in the toolbox of atomic physics was experimentally developed first to study interacting bosonic atoms where an equal Rashba-Dresselhaus (ERD) artificial spin-orbit coupling was created [3]. It was suggested that interacting fermions could be studied using the same technique [3,4]. Estimulated by the dense literature of the effects of Rashba spin-orbit coupling (SOC) encountered in condensed matter physics [1,2], several theoretical groups investigated the effects of Rashba SOC for interacting ultra-cold fermions using mean field theories [5][6][7][8] or for interacting bosons [9,10]. Unfortunately, the experimental study of Rashba SOC requires more lasers and further developments are necessary to overcome several difficulties [11]. Thus, presently, artificial Rashba SOC has not yet been created in the context of ultra-cold atoms. However, simultaneous theoretical studies of superfluidity for the experimentally relevant ERD spin-orbit coupling were performed for ultra-cold bosons by others [12,13] and for ultra-cold fermions by our group [14][15][16].One of the benchmarks of experimental studies of Fermi superfluidity of cold atoms without artificial spinorbit coupling was the emergence of molecular bound states via the use of Feshbach resonances [17], which lead to the formation of molecules [18] To address the important issue of the emergence of Feshbach molecules for interacting fermions in the presence of artificial SOC and Zeeman fields, we start from the Hamiltonian for two non-interacting fermionswritten as the sum of two contributions, which have the generic form (withh = 1)The term containing h R = v R k x e y −k ...

Superfluid transition temperature and fluctuation theory of spin-orbit and Rabi coupled fermions with tunable interactions

“…For fixed spin-orbit coupling (Rabi field) and increasing Rabi field (spin-orbit coupling) two-body bound states emerge at larger (smaller) scattering parameters. These shifts are in agreement with the calculated shifts in binding energies of Feshbach molecules in the presence of equal Rashba-Dresselhaus spin-orbit coupling and Rabi fields [24,25].…”

“…The anisotropy of the effective bosonic masses, M x = M y = M z ≡ M ⊥ stems from the anisotropy of the equal Rashba-Dresselhaus spin-orbit coupling, which together with the Rabi coupling modifies the dispersion of the constituent fermions along the x direction. In the limit k F a s 1 the many-body effective masses reduce to those obtained by expanding the two-body binding energy E bs (q) ≈ −E b + q 2 /2M , and agree with known results [24,25]. However, for 1/k F a s 2, many-body and thermal effects produce deviations from the twobody result.…”

“…is the number of fermions in bound states, where n B (ω) = 1/(e βω − 1) is the Bose distribution function, E bs (q) is the energy of the bound states obtained from Γ −1 (q, z = E − 2µ) = 0, corresponding to a pole in the scattering amplitude Γ(q, z). In the limit of large and negative fermion chemical potential, the system becomes non-degenerate and Γ −1 (q, z) = 0 becomes the exact eigenvalue equation for the two-body bound state in the presence of spin-orbit and Rabi coupling [24,25]. The total number of fermions, as a function of µ, thus becomes…”

Enhanced Fermion Pairing and Superfluidity by an Imaginary Magnetic Field

“…For case (I), we have carried out the two-body and many-body calculations for the pairing and superfluidity therein, which also show enhancement by IMF; see Figure 4. In particular, with an IMF, the two-body bound state can form even in the weak coupling regime with 1/ a s <0, in contrary to the case of RMF where it can only appear in the molecule side with 1/ a s >0 (Williams et al., 2013, Zhang et al., 2013, Kurkcuoglu and de Melo, 2016); see Figure 4A. In Figure 4B, we plot the critical 1/asc for the bound-state formation as a function of | B |, and we see that the larger the IMF is, the weaker is the coupling (i.e., smaller 1/asc) required to afford a bound state, whereas the RMF displays an opposite trend.…”

Tuning Feshbach resonances in cold atomic gases with interchannel coupling

“…Previous studies have shown that FRs can be modified either by dressing the molecular bound state in the closed channel [2][3][4][5][6][7][8][9], or by coupling different atomic states in the open channel [10][11][12][13][14]. Under these situations, the resonance position as well as the atomic scattering length can be tuned by additional parameters.…”