We discuss the experimental engineering of model systems for the description of QED in one spatial dimension via a mixture of bosonic $^{23}$Na and fermionic $^6$Li atoms. The local gauge symmetry is realized in an optical superlattice, using heteronuclear boson-fermion spin-changing interactions which preserve the total spin in every local collision. We consider a large number of bosons residing in the coherent state of a Bose-Einstein condensate on each link between the fermion lattice sites, such that the behavior of lattice QED in the continuum limit can be recovered. The discussion about the range of possible experimental parameters builds, in particular, upon experiences with related setups of fermions interacting with coherent samples of bosonic atoms. We determine the atomic system's parameters required for the description of fundamental QED processes, such as Schwinger pair production and string breaking. This is achieved by benchmark calculations of the atomic system and of QED itself using functional integral techniques. Our results demonstrate that the dynamics of one-dimensional QED may be realized with ultracold atoms using state-of-the-art experimental resources. The experimental setup proposed may provide a unique access to longstanding open questions for which classical computational methods are no longer applicable.
In this review article, we present the recent theoretical developments and some breakthrough experiments in cavity QED systems (optical and optomechanical systems) and also focus on the experimental realization of the theoretical proposals.
Recently, there has been much interest in simulating quantum field theory effects of matter and gauge fields. In a recent work [Phys. Rev. Lett. 107, 275301 (2011)] a method for simulating compact Quantum Electrodynamics (cQED) using Bose-Einstein condensates has been suggested. We suggest an alternative approach, which relies on single atoms in an optical lattice, carrying 2l+1 internal levels, which converges rapidly to cQED as l increases. That enables the simulation of cQED in 2+1 dimensions in both the weak and the strong coupling regimes, hence allowing to probe confinement as well as ot…
We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [PRA 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flo…
Supersymmetric systems derive their properties from conserved supercharges which form a supersymmetric algebra. These systems naturally factorize into two subsystems, which, when considered as individual systems, have essentially the same eigenenergies, and their eigenstates can be mapped onto each other. We first propose a one-dimensional ultracold atom setup to realize such a pair of supersymmetric systems. We propose a Mach-Zehnder interference experiment which we demonstrate for this system, and which can be realized with current technology. In this interferometer, a single atom wave packe…
Gauge fields are ubiquitous in nature. In the context of quantum electrodynamics, you may be most familiar with the photon, which represents the gauge field mediating electromagnetic forces. But there are also gluons, which mediate strong forces, and the W and Z particles, which mediate the weak forces. According to the standard model, those few gauge bosons, in fact, mediate all elementary interactions.
We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as well as 2d flux loops deformations and breaking, and to observe Wilson-loop area-law.
In this article, a method is proposed to spatially scale up a trapped ultracold gas while conserving the quantum correlations of the initial many-body state. For systems supporting self-similar dynamics, this is achieved by implementing a many-body finite-time frictionless quantum quench of the harmonic trap which acts as a quantum dynamical microscope.
All light has structure, but only recently it has become possible to construct highly controllable and precise potentials so that most laboratories can harness light for their specific applications. In this chapter, we review the emerging techniques for high-resolution and configurable optical trapping of ultracold atoms. We focus on optical deflectors and spatial light modulators in the Fourier and direct imaging configurations. These optical techniques have enabled significant progress in studies of superfluid dynamics, single-atom trapping, and underlie the emerging field of atomtronics. Th…
We propose a method for simulating 2+1-d compact lattice quantum-electrodynamics (QED), using ultracold atoms in optical lattices. In our model local Bose-Einstein condensates' phases correspond to the electromagnetic vector-potential, and the fluctuations of the local number operators represent the conjugate electric field. The gauge invariant Kogut-Susskind Hamiltonian is obtained as an effective low energy theory. The field is then coupled to external static charges. We show that in the strong coupling limit this gives rise to 'electric flux-tubes' and to confinement. The effect can be obse…
We consider a system of ultracold atoms in an optical lattice as a quantum simulator for electron-positron pair production in quantum electrodynamics (QED). For a setup in one spatial dimension, we investigate the nonequilibrium phenomenon of pair production including the backreaction leading to plasma oscillations. Unlike previous investigations on quantum link models, we focus on the infinite-dimensional Hilbert space of QED and show that it may be well approximated by experiments employing Bose-Einstein condensates interacting with fermionic atoms. The calculations based on functional integ…
Optimizing two-qubit gates for ultracold fermions in optical lattices
Forschungszentrum Jülich GmbH（于利希研究中心）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文系）
Ultracold dilute gases provide ideal settings for measurements of atomic structure. Helium has an internal structure sufficiently simple to permit highly accurate predictions of its resonances and transition rates. Precise laser spectroscopy of helium thus yields empirical constraints on such calculations. These are desirable in the ongoing investigations seeking to reconcile the disagreement between independent determinations of nuclear charge radius data in both hydrogenic and helium atoms. Either the size of these particles are truly constant and quantum electrodynamics (QED) is flawed, or …
The formulation of massless relativistic fermions in lattice gauge theories is hampered by the fundamental problem of species doubling, namely, the rise of spurious fermions modifying the underlying physics. A suitable tailoring of the fermion masses prevents such abundance of species, and leads to the so-called Wilson fermions. Here we show that ultracold atoms provide us with the first controllable realization of these paradigmatic fermions, thus generating a quantum simulator of fermionic lattice gauge theories. We describe a novel scheme that exploits laser-assisted tunneling in a cubic op…
Quantum simulation has the potential to investigate gauge theories in strongly-interacting regimes, which are up to now inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based method for studying $\mathbb{Z}_2$ lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits $\mathbb{Z}_2$ symmetry. We study the dynamics of the system…
We propose a minimal model to study the real-time dynamics of a $\mathbb{Z}_2$ lattice gauge theory coupled to fermionic matter in a cold atom quantum simulator setup. We show that dynamical correlators of the gauge fields can be measured in experiments studying the time-evolution of two pairs of impurities, and suggest the protocol for implementing the model in cold atom experiments. Further, we discuss a number of unexpected features found in the integrable limit of the model, as well as its extensions to a non-integrable case. A potential experimental implementation of our model in the latt…
We propose a scheme to measure the quantized Hall conductivity of an ultracold Fermi gas initially prepared in a topological (Chern) insulating phase, and driven by a constant force. We show that the time evolution of the center of mass, after releasing the cloud, provides a direct and clear signature of the topologically invariant Chern number. We discuss the validity of this scheme, highlighting the importance of driving the system with a sufficiently strong force to displace the cloud over measurable distances while avoiding band-mixing effects. The unusual shapes of the driven atomic cloud…
Ultracold atomic systems offer a unique tool for understanding behavior of matter in the quantum degenerate regime, promising studies of a vast range of phenomena covering many disciplines from condensed matter to quantum information and particle physics. Coupling these systems to quantized light fields opens further possibilities of observing delicate effects typical of quantum optics in the context of strongly correlated systems. Measurement backaction is one of the most fundamental manifestations of quantum mechanics and it is at the core of many famous quantum optics experiments. Here we s…
Ultracold Fermi gases trapped in honeycomb optical lattices provide an intriguing scenario, where relativistic quantum electrodynamics can be tested. Here, we generalize this system to non-Abelian quantum electrodynamics, where massless Dirac fermions interact with effective non-Abelian gauge fields. We show how in this setup a variety of topological phase transitions occur, which arise due to massless fermion pair production events, as well as pair annihilation events of two kinds: spontaneous and strongly-interacting induced. Moreover, such phase transitions can be controlled and characteriz…
We present a general scheme for synthesizing a spatially periodic magnetic field, or a magnetic lattice (ML), for ultracold atoms using pulsed gradient magnetic fields. Both the period and the depth of the artificial ML can be tuned, immune to atomic spontaneous emission often encountered in optical lattices. The effective Hamiltonian for our 2-dimensional ML has not been discussed previously in condensed matter physics. Its band structures show interesting features which can support topologically nontrivial phases. The technical requirements for implementing our protocol are readily available…
We report the experimental observation of tunable, non-reciprocal quantum transport of a Bose-Einstein condensate in a momentum lattice. By implementing a dissipative Aharonov-Bohm (AB) ring in momentum space and sending atoms through it, we demonstrate a directional atom flow by measuring the momentum distribution of the condensate at different times. While the dissipative AB ring is characterized by the synthetic magnetic flux through the ring and the laser-induced loss on it, both the propagation direction and transport rate of the atom flow sensitively depend on these highly tunable parame…
Few-Photon Fluorescence from Ultracold Bosons in an Optical Cavity
Lund University（隆德大学）；RNS Institute of Technology (Affilated to Visvesvaraya Technological University)（RNS理工学院（隶属于维斯瓦萨拉亚技术大学））；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构和动力学研究所）；Universidad del Pais Vasco（巴斯克大学）
One of the paradigms of a small quantum system in a dissipative environment is the decay of an excited atom undergoing spontaneous photon emission into the fluctuating quantum electrodynamic vacuum. Recent experiments have demonstrated that the gapped photon dispersion in periodic structures can give rise to novel spontaneous-decay behavior including the formation of dissipative bound states. So far, these effects have been restricted to the optical domain. Here, we experimentally demonstrate similar behavior in a system of artificial atoms in an optical lattice that decay by emitting matter-w…
Towards $2+1$D quantum electrodynamics on a cold-atom quantum simulator
Università di Padova（帕多瓦大学）；Padua Quantum Technologies Research Center, Università degli Studi di Padova（帕多瓦量子技术研究中心，帕多瓦大学）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova（意大利国家核物理研究所（INFN），帕多瓦分部）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Ludwig Maximilian University of Munich（慕尼黑路德维希-马克西米利安大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of Trento（特伦托大学）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（INFN-TIFPA，特伦托基础物理与应用研究所）；Southern University of Science and Technology（南方科技大学）
We examine the dynamics of ultracold atoms held in optical lattice potentials. By controlling the switching of a periodic driving potential we show how a phase-induced renormalization of the intersite tunneling can be used to produce directed motion and control wavepacket spreading. We further show how this generation of a synthetic gauge potential can be used to split and recombine wavepackets, providing an attractive route to implementing quantum computing tasks.
A phenomenon can hardly be found that accompanied physical paradigms and theoretical concepts in a more reflecting way than magnetism. From the beginnings of metaphysics and the first classical approaches to magnetic poles and streamlines of the field, it has inspired modern physics on its way to the classical field description of electrodynamics, and further to the quantum mechanical description of internal degrees of freedom of elementary particles. Meanwhile, magnetic manifestations have posed and still do pose complex and often controversially debated questions. This regards so various and…
We present a simple scheme for implementing a one-dimensional (1D) magnetic-flux lattice of ultracold fermionic spin-$1/2$ atoms. The resulting tight-binding model supports gapped and gapless topological phases, and chiral currents for Meissner and vortex phases. Its single-particle spectra exhibit topological flat bands at small flux, and the flatness sensitively depends on hopping strength. An effective $p$-wave interaction arises in a $s$-wave paired superfluid. Treating atomic internal states as forming a synthetic dimension and balancing the interplay of magnetic flux and Zeeman field, ou…
Constructing Arbitrary Coherent Rearrangements in Optical Lattices
Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Fakultät für Physik, Ludwig-Maximilians-Universität（慕尼黑大学物理学院）；Department of Physics and SUPA, University of Strathclyde（斯特拉斯克莱德大学物理与SUPA学院）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Recent years have seen tremendous progress in creating complex atomic many-body quantum systems. One approach is to use macroscopic, effectively thermodynamic ensembles of ultracold atoms to create quantum gases and strongly correlated states of matter, and to analyze the bulk properties of the ensemble. The opposite approach is to build up microscopic quantum systems atom by atom - with complete control over all degrees of freedom. Until now, the macroscopic and microscopic strategies have been fairly disconnected. Here, we present a "quantum gas microscope" that bridges the two approaches, r…
Parallel analog quantum simulation in homogeneous quantum gases
Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所）；European Laboratory for Nonlinear Spectroscopy (LENS), University of Florence（佛罗伦萨大学欧洲非线性光谱学实验室）；Department of Physics, University of Florence（佛罗伦萨大学物理系）；National Institute for Metrological Research (INRiM)（国家计量研究所）
We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent- and/or co-walking dependent on both quantum statistics and interaction strength. We find that two strongly interacting particles may form a bound state and then co-walk like a single composite particle with statistics-dependent propagation speed. Such an effective single-particle picture of co-walking is analytically derived in the context of degenerate pertu…
Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum simulation of lattice gauge theories, however, hinges crucially on the efficient use of experimental resources. As we argue in this work, due to the fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian, the lattice representation of gauge theories allows for an optimization that up to now has been left unexplored. We exemplify our discussion…
In quantum interferometry, it is vital to control and utilize nonlinear interactions for achieving high-precision measurements. Attribute to their long coherent time and high controllability, ultracold atoms including Bose condensed atoms have been widely used for implementing quantum interferometry. Here, we review the recent progresses in theoretical studies of quantum interferometry with Bose condensed atoms. In particular, we focus on the nonlinear phenomena induced by the atom-atom interaction and how to control and utilize these nonlinear phenomena. Under the mean-field description, due …
The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified \textit{local pseudogenerators} designed such that within the physical sector they act id…
Fermions are the building blocks of matter, forming atoms and nuclei, complex materials and neutron stars. Our understanding of many-fermion systems is however limited, as classical computers are often insufficient to handle the intricate interplay of the Pauli principle with strong interactions. Quantum simulators based on ultracold fermionic atoms instead directly realize paradigmatic Fermi systems, albeit in "analog" fashion, without coherent control of individual fermions. Digital qubit-based quantum computation of fermion models, on the other hand, faces significant challenges in implemen…
