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arXiv:2008.02412 · Physical Review A

Artificial magnetic field for synthetic quantum matter without dynamical modulation

Tomoki Ozawa

Published Mar 19, 2021• 6 citations
arXivHTMLPDF

Abstract

We propose an all-static method to realize an artificial magnetic field for charge neutral particles without introducing any time modulation. Our proposal consists of one-dimensional tubes subject to harmonic trapping potentials with shifted centers. We show that this setup realizes an artificial magnetic field in a hybrid real-momentum space. We discuss how characteristic features of particles in a magnetic field, such as chiral edge states and the quantized Hall response, can be observed in this setup. We find that the mean-field ground state of bosons in this setup in the presence of long-range interactions in physical real space can have quantized vortices in the hybrid real-momentum space; such a state with vortices exhibits a supersolid structure in the physical real space. Our method can be applied to a variety of synthetic quantum matter, including ultracold atomic gases, coupled photonic cavities, coupled waveguides, and exciton-polariton lattices.

DOI
10.1103/physreva.103.033318

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We propose an all-static method to realize an artificial magnetic field for charge neutral particles without introducing any time modulation. Our proposal consists of one-dimensional tubes subject to harmonic trapping potentials with shifted centers. We show that this setup realizes an artificial magnetic field in a hybrid real-momentum space. We discuss how characteristic features of particles in a magnetic field, such as chiral edge states and the quantized Hall response, can be observed in this setup. We find that the mean-field ground state of bosons in this setup in the presence of long-range interactions in physical real space can have quantized vortices in the hybrid real-momentum space; such a state with vortices exhibits a supersolid structure in the physical real space. Our method can be applied to a variety of synthetic quantum matter, including ultracold atomic gases, coupled photonic cavities, coupled waveguides, and exciton-polariton lattices.
Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.
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.
We introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realization of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.
Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.
Chiral edge states are a hallmark of quantum Hall physics. In electronic systems, they appear as a macroscopic consequence of the cyclotron orbits induced by a magnetic field, which are naturally truncated at the physical boundary of the sample. Here we report on the experimental realization of chiral edge states in a ribbon geometry with an ultracold gas of neutral fermions subjected to an artificial gauge field. By imaging individual sites along a synthetic dimension, encoded in the nuclear spin of the atoms, we detect the existence of the edge states and observe the edge-cyclotron orbits induced during quench dynamics. The realization of fermionic chiral edge states opens the door for edge state interferometry and the study of non-Abelian anyons in atomic systems.
Cold atomic gases are perfect laboratories for realization of quantum simulators. In order to simulate solid state systems in the presence of magnetic fields special effort has to be made because atoms are charge neutral. There are different methods for realization of artificial magnetic fields, that is the creation of specific conditions so that the motion of neutral particles mimics the dynamics of charged particles in an effective magnetic field. Here, we consider adiabatic motion of atoms in the presence of an evanescent wave. Theoretical description of the adiabatic motion involves artificial vector and scalar potentials related to the Berry phases. Due to the large gradient of the evanescent field amplitude, the potentials can be strong enough to induce measurable effects in cold atomic gases. We show that the resulting artificial magnetic field is able to induce vortices in a Bose-Einstein condensate trapped close to a surface of a prism where the evanescent wave is created. We also analyze motion of an atomic cloud released from a magneto-optical trap that falls down on the surface of the prism. The artificial magnetic field is able to reflect falling atoms that can be observed experimentally.