Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultrastructure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the center-of-mass momentum of the colliding pair, we elucidate the relation between mean-field interactions and physical three-dimensional scattering lengths. As a consequence of infrared logarithmic divergences in the two-particle propagator, the effective interaction vanishes as the center-of-mass momentum approaches zero.
Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultrastructure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the center-of-mass momentum of the colliding pair, we elucidate the relation between mean-field interactions and physical three-dimensional scattering lengths. As a consequence of infrared logarithmic divergences in the two-particle propagator, the effective interaction vanishes as the center-of-mass momentum approaches zero.
We study ultracold bosons in three dimensions with an anisotropic Rashba-Dresselhaus spin-orbit coupling. We first carry out the exact summation of ladder diagrams for the two-boson t matrix at zero energy. Then, with the t matrix as the effective interaction, we find the ground-state phase diagrams of bosons in mean field as a function of the spin-orbit coupling, the anisotropy, and the scattering lengths between particles in the same and in different pseudospin states. The resulting phase diagrams have much richer structures than those obtained using mean-field couplings, exhibiting three different phases: a plane-wave condensate, a striped condensate, and an unstable phase. The differences between the present approach using the t matrix compared to using mean-field couplings is significant for large scattering lengths, large spin-orbit-coupling strength, or small anisotropy.
Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin-orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin-orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose-Einstein condensate (RBEC) is a quite intriguing state with the rashbon-rashbon interactions being independent of the fermion-fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin-orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.
Two-body scattering constitutes one of the most fundamental processes in various physical systems ranging from ultracold dilute quantum gases to energetic quark- gluon plasmas. In this dissertation, we study the low-energy atomic collision physics in the presence of synthetic gauge fields, which are generated by atom-light interaction. One category of synthetic gauge fields is the artificial spin-orbit coupling. We discuss three different aspects in scattering theory: ultracold collision, scattering resonance, and bound state formation from a few-body perspective when the atomic spin states are coupled with their center-of-mass motion. The understanding of the spin-orbit effects on the modification of the scattering processes not only builds the foundation of collision physics in the presence of non-abelian gauge fields but also paves the way towards unraveling the few-body correlations in many-body systems.
We studied the influence of spin-orbit interaction (SOI) in interacting low dimensional quantum systems at zero temperature within the framework of the functional renormalization group (fRG). Among the several types of spin-orbit interaction the so-called Rashba spin-orbit interaction is especially intriguing for future spintronic applications as it may be tuned via external electric fields. We investigated its effect on the low energy physics of an interacting quantum wire in an applied Zeeman field which is modeled as a generalization of the extended Hubbard model. To this end we performed a renormalization group study of the two particle interaction, including the SOI and the Zeeman field exactly on the single particle level. Considering the resulting two band model, we formulated the RG equations for the two particle vertex keeping the full band structure as well as the non trivial momentum dependence of the low energy two particle scattering processes. In order to solve these equations numerically we defined criteria that allowed us to classify whether a given set of initial conditions flows towards the strongly coupled regime. We found regions in the models parameter space where a weak coupling method as the fRG is applicable and it is possible to calculate additional quantities of interest. Furthermore we analyzed the effect of the Rashba SOI on the properties of an interacting multi level quantum dot coupled to two semi innite leads. Of special interest was the interplay with a Zeeman field and its orientation with respect to the SOI term. We found a renormalization of the spin-orbit energy which is an experimental quantity used to asses SOI effects in transport measurements, as well as renormalized effective g factors used to describe the Zeeman field dependence. In particular in asymmetrically coupled systems the large parameter space allows for rich physics which we studied by means of the linear conductance obtained via the generalized Landauer-Büttiker formalism from the renormalized self energy. The multi level quantum dot exhibits Kondo physics at finite Zeeman fields which can be suppressed if the field and the SOI term are not aligned in parallel. Due to broken particle hole symmetry we observed a gate voltage dependence for finite field conductance plateaus. The computed dependencies have been observed in experiments and thus highlight the flexibility of the considered model. Finally we computed the linear conductance for a multi level quantum dot model that has been proposed to describe SOI and impurity scattering effects in carbon nanotubes (CNT). The SOI was seen to affect the already complicated level structure of the CNT and thus profoundly changes the linear conductance, especially the location of conductance resonances with respect to an applied magnetic field and gate voltage. Again asymmetries influence the conductance and the effects are explained by means of the effective tunnel couplings to the eigenstates of the CNT. We finished with an improved analysis of a reduced version of this model that includes two particle vertex renormalization. The computed linear conductance is in excellent agreement with experimental data.
Thanks to the recent experimental realization and control of artificial gauge fields, spin-orbit (SO) couplings are witnessing an ever increasing interest in the field of cold atoms. However, predicting their effect on spin polarization and energetic properties of interacting systems is a major challenge, due to the complex interplay between spin and position dynamics. In this work we exploit the diffusion Monte Carlo algorithm to compute energetic and polarization properties of a three-dimensional repulsive Fermi gas in the presence of Rashba spin-orbit coupling. We find that SO effects tend to contrast the spin alignment induced by the exchange interaction, slightly shifting the onset of the Stoner instability towards larger values of the scattering length. In addition, polarization and energy properties of the system can be tuned trough a combined control of the repulsive interaction and Rashba coupling.
In this thesis, we present theoretical studies on three topics related to multi-component ultracold gases and gauge fields. The first topic that we discuss is artificial gauge fields in ultracold gases. Recently, methods to create artificial gauge fields coupled to neutral ultracold systems using a light-induced Berry's connection have been rapidly developing. These methods are not only capable of creating Abelian gauge fields, such as a conventional magnetic field, but also non-Abelian gauge fields, which opens a way to explore and simulate a wide variety of physical models. In this thesis, we discuss various properties of bosons with Rashba-Dresselhaus spin-orbit coupling, which is a special type of non-Abelian gauge field. We investigate the stability of Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling, and show that the condensates are stable against quantum and thermal fluctuations. We also consider the renormalization of the bare interaction by calculating the t-matrix and its consequence on the ground state phase diagrams. The second topic discussed here is three-component ultracold fermionic systems. It is known that ferromagnetism and superfluidity can coexist at low enough temperature in three-component ultracold fermions. In this thesis, we elucidate how fermionic pairing and population imbalance enhance each other. We also describe a crossover from Bardeen-Cooper-Schrieffer state of fermionic pairing state to the limit of Bose-Einstein condensate of three weakly interacting species of molecules, as the interaction increases. Furthermore, we find an interesting similarity in the free energies between three-component ultracold fermions and quantum chromodynamics. The last topic discussed here is Niels Bohr's double-slit interference gedankenexperiment with charged particles, which argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances. Under these conditions the interference pattern must be suppressed; otherwise quantum mechanics is not consistent. The mechanism for the suppression of the interference pattern is that, as the particle's trajectory is bent in diffraction by the slits, it must radiate and the radiation must carry away phase information. Thus, the radiation field must be a quantized dynamical degree of freedom. We also consider the related setup in which one attempts to determine the path of a massive particle through an interferometer by measuring the Newtonian gravitational potential the particle produces. In this case, we show that the interference pattern would have to be finer than the Planck length and thus indiscernible. Therefore, unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.