Abstract The past few years have seen fascinating progress in the creation and utilization of synthetic gauge fields for charge-neutral ultracold atoms. Whereas the synthesis of gauge fields in itself is readily interesting, it is more exciting to explore the new era that will be brought by the interplay between synthetic gauge fields and many other degrees of freedom of highly tunable ultracold atoms. This topical review surveys recent developments in using synthetic gauge fields to manipulate novel quantum phenomena that are not easy to access in other systems. We first summarize current experimental methods of creating synthetic gauge fields, including the use of Raman schemes, shaken lattices, and Raman-dressed lattices. We then discuss how synthetic gauge fields bring new physics to non-interacting systems, including degenerate single-particle ground states, quartic dispersions, topological band structures in lattices, and synthetic dimensions. As for interacting systems, we focus on novel quantum many-body states and quantum macroscopic phenomena induced by interactions in the presence of unconventional single-particle dispersions. For bosons, we discuss how a quartic dispersion leads to non-condensed bosonic states at low temperatures and at the ground state. For fermions, we discuss chiral superfluids in the presence of attractive s-wave interaction, where high partial-wave interactions are not required. Finally, we discuss the challenges in current experiments, and conclude with an outlook for what new exciting developments synthetic gauge fields may bring us in the near future.
Abstract The past few years have seen fascinating progress in the creation and utilization of synthetic gauge fields for charge-neutral ultracold atoms. Whereas the synthesis of gauge fields in itself is readily interesting, it is more exciting to explore the new era that will be brought by the interplay between synthetic gauge fields and many other degrees of freedom of highly tunable ultracold atoms. This topical review surveys recent developments in using synthetic gauge fields to manipulate novel quantum phenomena that are not easy to access in other systems. We first summarize current experimental methods of creating synthetic gauge fields, including the use of Raman schemes, shaken lattices, and Raman-dressed lattices. We then discuss how synthetic gauge fields bring new physics to non-interacting systems, including degenerate single-particle ground states, quartic dispersions, topological band structures in lattices, and synthetic dimensions. As for interacting systems, we focus on novel quantum many-body states and quantum macroscopic phenomena induced by interactions in the presence of unconventional single-particle dispersions. For bosons, we discuss how a quartic dispersion leads to non-condensed bosonic states at low temperatures and at the ground state. For fermions, we discuss chiral superfluids in the presence of attractive s-wave interaction, where high partial-wave interactions are not required. Finally, we discuss the challenges in current experiments, and conclude with an outlook for what new exciting developments synthetic gauge fields may bring us in the near future.
Ultracold gases are remarkably versatile and controllable systems with untapped potential to emulate a variety of quantum phenomena [1]. Atoms are, however, electrically neutral and therefore it is highly desirable to make them behave as charged particles. This capability has recently been demonstrated in a series of recent experiments [2–4]. Although many challenges remain ahead, atoms exposed to synthetic gauge field offer great opportunities for the realization of new classes of quantum materials with custom-designed properties, and with unforeseen applications. The first implementation of an effective magnetic field was accomplished by rotating an atomic cloud [5]. In the rotating frame of reference, an atom experiences the Coriolis force that emulates the Lorentz force experienced by a charged particle in a uniform magnetic field. Large vortex lattices have been created in this way, however, so far the strength of the effective magnetic field achieved by rotation is too weak to lead to new physics. An alternative approach invokes the vector potential, A, that induces a geometric phase as a charged particle moves around a closed loop. This notion of geometric phase can be adapted to a neutral atom that slowly moves in the presence of laser fields. If the lasers are chosen to ‘dress’ the internal atomic levels, so that the dressed eigenstates become position dependent, the center of mass adiabatically evolves according the operator p-A, instead of just p = −iℏ∇. The atom thus effectively moves as a charged particle in a magnetic field B = ∇ × A (see Fig. 1a). Exploiting this idea series of experiments have implemented artificial magnetic and electric fields [2–4]. The idea has also been implemented in the presence of a superimposed periodic optical lattice potential (see Fig. 1b). In this case, the length scale imposed by the lattice competes with the one associated with the magnetic field and can lead to frustration, manifested as an energy spectrum with fractal characteristics [2,3]. Light induced synthetic gauge fields: (a) A gas of neural atoms (green oval) can behave as a gas of charged particles when it is illuminated by a pair of laser beams (red arrows) that imparts momentum to the atoms and couples their internal (.|↑.〉, .|↓.〉) and motional degrees of freedom. The Raman beams that induce transitions between internal states also transfer two units of their linear momentum 2kL. This leads to the formation of dressed states (superpositions of states with different internal levels and center of mass momenta) which experience a modified kinetic energy, with an effective vector potential. If the effective vector potential has nonzero curl, the atoms move as charged particles in a magnetic field. (b) In the presence of an optical lattice potential, Raman beams can also induce an effective vector potential. In this case, the lattice is engineered so that along one direction atoms can tunnel between adjacent lattice sites (Jlight) only by absorbing and emitting photons from the beams. The imparted momentum from the lasers produces path-dependent phases that resemble the magnetic flux accumulated by a charged particle as it moves in a closed loop. The flux accumulated by the atoms when they move around a single unit cell, ϕ, can be significant (equivalent to the one generated by a real magnetic field of thousands tesla in an electronic system) and induce a fractal energy spectrum. Generalizations to emulate non-Abelian gauge potentials, associated in many cases to spin-orbit coupling can emerge when the geometric phase is replaced by a matrix acting on the internal Hilbert space [2–5]. This happens if there is a manifold of degenerate dressed states, such that even for arbitrarily slow motion, after traveling around a contour the particle ends up in a different internal state. Although various proposals for generating non-Abelian potentials exist, they remain to be implemented. On the other hand, Abelian spin-orbit coupling, arising from the momentum kicks imparted on the atom by the laser photons that drive internal transitions, has been realized in several laboratories using different laser configurations in alkali-metal (one outer electron) and alkaline-earth (two outer electrons) atoms [2–5]. There is a great vista ahead. For example, the inclusion of collisions or dipolar interactions will open a window to engineer fractional Hall liquids, unconventional superfluids and interacting topological phases. The creation of dynamical gauge fields important in many areas of physics such as quantum chromodynamics is also an open direction. The time is just ripe for investigating rich and unexplored physics with synthetic gauge fields for ultracold matter.
Quantum emulation property of the cold atoms has generated a lot of interest in studying systems with synthetic gauge fields. In this article, we describe the physics of two component Fermi gas in the presence of synthetic non-Abelian SU(2) gauge fields. Even for the non-interacting system with the gauge fields, there is an interesting change in the topology of the Fermi surface by tuning only the gauge field strength. When a trapping potential is used in conjunction with the gauge fields, the non-interacting system has the ability to produce novel Hamiltonians and show characteristic change in the density profile of the cloud. Without trap, the gauge fields act as an attractive interaction amplifier and for special kinds of gauge field configurations, there are two-body bound states for any attraction even in three dimensions. For a many body system, the gauge fields can induce a crossover from a weak superfluid to a strong superfluid with transition temperature as high as the Fermi temperature. The superfluid state obtained for a very large gauge field strength is a superfluid of new kind of bosons, called ``rashbons'', the properties of which are independent of its constituent two component fermions and are solely determined by the gauge field strength. We also discuss the collective excitations over the superfluid ground states and the experimental relevance of the physics.
Abelian and non-Abelian gauge potentials and quantum gauge theories play central roles in our understanding of Nature. Gauge potentials are also of great significance in condensed matter physics. In fact, minimal coupling of electrons to an Abelian or non-Abelian gauge potential is the essential ingredient for the realization of topological states of matter. Due to the high controllability of ultracold atoms, they are commonly exploited to test fundamental theories of physics, simulate intractable systems, and realize exotic many-body states. Nonetheless, the charge neutrality of atoms places severe constraints on ultracold atomic systems, since neutral particles do not couple to gauge potentials the way charged particles do. That said, coupling a multi-component quantum gas to laser light can lead to the emergence of artificial Abelian and non-Abelian gauge potentials minimally coupled to the center-of-mass momenta of ultracold neutral atoms, paving the way for realizing topological states of matter and simulating gauge theories in quantum gases. All previous proposals for inducing gauge potentials have been developed in the semiclassical regime, where the radiation field is treated classically. I have developed a two-photon Raman scheme in the strong atom-photon coupling (i.e., quantum) regime, based on two counter-propagating modes of a ring cavity, to induce both synthetic magnetic field and spin-orbit coupling for a single neutral atom inside the cavity. The spin-orbit interaction is only weakly dependent on the occupation of the cavity modes, whereas the strength of the magnetic field is proportional to the square of the total number of photons in the cavity and can be made arbitrarily large, which is desirable for realizing the quantum Hall phase. I have then extended this single-atom cavity quantum-electrodynamics scheme to many bosons in the weak atom-photon coupling regime. In addition to inducing spin-orbit coupling for the individual atoms, the cavity fields also mediate infinite-ranged interactions between atoms, whose strengths and signs can readily be tuned experimentally. The interplay between these cavity-mediated interactions and the intrinsic two-body interactions determines the many-body ground state and its elementary excitations, with novel consequences such as the stabilization of an attractive Bose-Einstein condensate which otherwise is unstable.
Ultracold atomic systems have provided an ideal platform to study the physics of strongly interacting many body systems in an unprecedentedly controlled and clean environment. And, since fermions are the building blocks of visible matter, being naturally motivated we focus on the physics of ultracold fermionic systems in this thesis. There have been many recent experimental developments in these systems such as the creation of synthetic gauge fields, realization of dimensional crossover and realization of systems with synthetic dimensions. These developments pose many open theoretical questions, some of which we address in this thesis.
We start the discussion by studying the spectral function of an ideal spin-12 Fermi gas in a harmonic trap in any dimensions. We discuss the performance of the local density approximation (LDA) in calculating the spectral function of the system by comparing it to exact numerical results. We show that the LDA gives better results for larger number of particles and in higher dimensions.
Fermionic systems with quasi two dimensional geometry are of great importance because of their connections to the high-Tc superconducting cuprate materials. Keeping this in mind, we consider a spin-12 fermionic system in three dimensions interacting with a contact interaction and confined by a one dimensional optical potential in one direction. Using the Bogoliubov-de Gennes formalism, we show that with increasing the depth of the optical potential the three dimensional superfluid evolves into a two dimensional one by looking at the shifts in the radio-frequency spectrum of the system and the change in the binding energy
of the pairs that are formed.
The next topic of interest is studying the effect of synthetic gauge fields on the ultracold fermionic systems. We show that a synthetic non-Abelian Rashba type gauge field has experimentally observable signatures on the size and shape of a cloud of a system of non-interacting spin-12 Fermi system in a harmonic trap. Also, the synthetic gauge field in conjunction with the harmonic potential gives rise to ample possibilities of generating novel quantum Hamiltonians like the spherical geometry quantum Hall, magnetic monopoles etc.
We then address the physics of fermions in “synthetic dimensions”. The hyperfine states of atoms loaded in a one dimensional optical lattice can be used as an extra dimension, called the synthetic dimension (SD), by using Raman coupling. This way a finite strip Hofstadter model is realized with a tunable flux per plaquette. The experimental realization of the SD system is most naturally possible in systems which also have SU(M) symmetric interactions between the fermions. The SU(M) symmetric interactions manifest as long-ranged along the synthetic dimension and is the root cause of all the novel physics in these systems. This rich physics is revealed by a mapping of the Hamiltonian of the system to a system of particles interacting via an SU(M) symmetric interaction under the influence of an SU(M) Zeeman field and a non-Abelian…
Synthetic gauge fields for ultracold neutral atoms-engineered using the interaction between laser fields and the atoms' internal 'spin' degrees of freedom-provide promising techniques for generating the large (synthetic) magnetic fields required to reach the fractional quantum Hall (FQH) limit in quantum gases, bosonic or fermionic alike.Because neutral atoms can move in a nearly disorder-free environment and they have extremely simple contact interactions, the resulting FQH states would be revealed in their most essential form.Moreover, bosonic FQH states represent a new frontier and have never been seen in any setting.Going beyond electromagnetismʼs conventional scalar gauge field, it is possible to create more general non-Abelian gauge potentials.When these are spatially uniform, they are equivalent to spin-orbit coupling familiar in material systems, and can lead to cold atom analogs of topological insulators and topological superconductors.In this tutorial, we introduce basic concepts underlying these gauge fields, making connections to the Aharonov-Bohm phase and geometric phase.We focus on the system of neutral atoms 'dressed' by multiple laser beams, where the eigenstates of the resulting Hamiltonian are known as dressed states.Synthetic gauge potentials arise from the unitary transformation required to express these dressed states in terms of the laser-free eigenstates.We discuss stability of laser-dressed atoms corresponding to the adiabatic condition and the probability of non-adiabatic transitions.Adopting both the semiclassical and quantum mechanical approaches, we demonstrate they agree in the suitable limit.We also analyze using both the conventional adiabatic picture and exact picture, where the kinetic energy is neglected in the former and retained in the latter picture.
This thesis considers novel phenomena arising in the few and many-body physics of ultracold atomic gases. The specific models considered are motivated by recent experimental developments. A main focus will be the theoretical description of systems used in the simulation of artificial gauge fields via time-modulated tuning of system parameters and via the coupling of internal atomic states by Raman lasers. A second aspect will be the study of systems with synthetic dimensions and the effects of the unconventional infinite range interactions that arise in this description. It explores time-dependent effects in the single and few particle setting and the collective many-body phases arising in these models. Using the framework of Floquet theory it studies the interplay of time-dependence and particle-interactions both in continuum and lattice systems. In particular, it provides a general explanation for how heating effects can arise in interacting periodically time-dependent quantum systems, identifying an underlying mechanism for heating via two-particle collisions and the relevant scaling of the associated rates with system parameters. Furthermore, the general framework is applied to specific experimental set-ups. This yields heating rates and population dynamics in agreement with the experimental data. Finally, it also proposes improvements to the experiment that allow to limit the heating rates which is required to access the strongly interacting regime. In the case of synthetic dimensions the focus lies on the intriguing interplay of artificial gauge fields and strong particle interactions of atoms confined in optical lattices. In these systems a suitable coupling of internal spin-states of the atoms allows to simulate an additional finite dimension. In contrast to the typically encountered situation of short-range interactions the particle interactions are infinite-range in this synthetic dimension. In the strong coupling limit an effective description for this system is derived and its ground state phase diagram is studied using numerical tools.