There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, ie, quantum simulation Quantum simulation promises to have applications in the study of many problems in, eg, condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins and photons have been proposed as quantum simulators This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field

Quantum Simulation

When a neutral atom moves in a properly designed laser field, its center-of-mass motion may mimic the dynamics of a charged particle in a magnetic field, with the emergence of a Lorentz-like force. In this Colloquium the physical principles at the basis of this artificial (synthetic) magnetism are presented. The corresponding Aharonov-Bohm phase is related to the Berry's phase that emerges when the atom adiabatically follows one of the dressed states of the atom-laser interaction. Some manifestations of artificial magnetism for a cold quantum gas, in particular, in terms of vortex nucleation are discussed. The analysis is then generalized to the simulation of non-Abelian gauge potentials and some striking consequences are presented, such as the emergence of an effective spin-orbit coupling. Both the cases of bulk gases and discrete systems, where atoms are trapped in an optical lattice, are addressed.

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Colloquium: Artificial gauge potentials for neutral atoms

Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.

https://iopscience.iop.org/article/10.1088/0034-4885/77/12/126401/pdf

Light-induced gauge fields for ultracold atoms

The basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field are reviewed. One of its most salient features is the relativistic quantum Hall effect, the observation of which has been the experimental breakthrough in identifying pseudorelativistic massless charge carriers as the low-energy excitations in graphene. The effect may be understood in terms of Landau quantization for massless Dirac fermions, which is also the theoretical basis for the understanding of more involved phenomena due to electronic interactions. The role of electron-electron interactions both in the weak-coupling limit, where the electron-hole excitations are determined by collective modes, and in the strong-coupling regime of partially filled relativistic Landau levels are presented. In the latter limit, exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states. Furthermore, the electron-phonon coupling in a strong magnetic field is discussed. Although the present review has a dominant theoretical character, a close connection with available experimental observation is intended.

Electronic properties of graphene in a strong magnetic field

We study the low-intensity light pulse propagation through an asymmetric double quantum well via Fano-type interference based on intersubband transitions. The propagation of the pulse across the quantum well is studied analytically and numerically with the coupled Maxwell-Schr\"odinger equations. We show the generation of ultraslow bright and dark optical solitons in this system. Whether the solitons are dark and bright can be controlled by the ratio of dipole moments of the intersubband transitions. Such investigation of ultraslow optical solitons in the present work may lead to important applications such as high-fidelity optical delay lines and optical buffers in semiconductor quantum wells structure.

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Ultraslow bright and dark solitons in semiconductor quantum wells

We show the possibility to generate bright and dark optical solitons based on bound-to-bound intersubband transitions in an asymmetric three-coupled quantum well structure. By presenting the concept of detuning management, we show that the bright optical soliton can evolve into a dark one by adiabatically changing the corresponding one- and two-photon detunings. With adjustable carrier frequencies within the terahertz regime, we also demonstrate numerically shape-recovered collisions of two solitons in our proposed quantum wells. The present investigation may provide research opportunities in nonlinear optical experiments and may have impact on the technology for the design of semiconductor devices.

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Detuning management of optical solitons in coupled quantum wells

We propose a scheme to simulate and observe massless Dirac fermions with cold atoms in a square optical lattice. A U(1) adiabatic phase is created by two laser beams for the tunneling of atoms between neighbor lattice sites. Properly adjusting the tunneling phase, we find that the energy spectrum has conical points in per Brillouin zone where band crossing occurs. Near these crossing points the quasiparticles and quasiholes can be considered as massless Dirac fermions. Furthermore, the anisotropic effects of massless Dirac fermions are obtained in the present square lattice model. The Dirac fermions as well as the anisotropic behaviors realized in our system can be experimentally detected with the Bragg spectroscopy technique.

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Massless Dirac fermions in a square optical lattice

We perform a time-dependent analysis of continuous wave (cw) four-wave mixing (FWM) in InGaAs/AlAs coupled double quantum well (CDQW) structures via intersubband transitions. By using the coupled Schrodinger-Maxwell approach, we obtain the corresponding explicit analytical expressions for the input probe and FWM-generated signal fields. We calculated the dependencies of the efficiency of the FWM-generated fields on cw pump fields and the depths of penetration into the CDQW sample. Such a nonlinear optical process may be used to generate coherent short-wavelength radiation efficiently in the CDQW solid state system.

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Highly efficient four-wave mixing via intersubband transitions in InGaAs/AlAs coupled double quantum well structures

We investigate the spectrum and eigenstates of ultracold fermionic atoms in the bilayer honeycomb optical lattice. In the low energy approximation the dispersion relation has parabolic form and the quasiparticles are chiral. In the presence of the effective magnetic field, which is created for the system with optical means, the energy spectrum shows an unconventional Landau level structure. Furthermore, the experimental detection of the spectrum is proposed with the Bragg scattering techniques.

Jing-Min Hou

Papers

Ultraslow bright and dark solitons in semiconductor quantum wells

Detuning management of optical solitons in coupled quantum wells

Massless Dirac fermions in a square optical lattice

Highly efficient four-wave mixing via intersubband transitions in InGaAs/AlAs coupled double quantum well structures

Energy bands and Landau levels of ultracold fermions in the bilayer honeycomb optical lattice