Quantum Many-body Physics Research Articles

Tunable-Range, Photon-Mediated Atomic Interactions in Multimode Cavity QED

Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic position. Specifically, we experimentally show that the interference of near-degenerate cavity modes leads to both a strong and tunable-range interaction between Bose-Einstein condensates (BECs) trapped within the cavity. We exploit the symmetry of a confocal cavity to measure the interaction between real BECs and their virtual images without unwanted contributions arising from the merger of real BECs. Atom-atom coupling may be tuned from short range to long range. This capability paves the way toward future explorations of exotic, strongly correlated systems such as quantum liquid crystals and driven-dissipative spin glasses.

Saturation of entropy production in quantum many-body systems.

Bridging the second law of thermodynamics and microscopic reversible dynamics has been a longstanding problem in statistical physics. Here, we address this problem on the basis of quantum many-body physics, and discuss how the entropy production saturates in isolated quantum systems under unitary dynamics. First, we rigorously prove that the entropy production does indeed saturate in the long time regime, even when the total system is in a pure state. Second, we discuss the non-negativity of the entropy production at saturation, implying the second law of thermodynamics. This is based on the eigenstate thermalization hypothesis, which states that even a single energy eigenstate is thermal. We also numerically demonstrate that the entropy production saturates at a non-negative value even when the initial state of a heat bath is a single energy eigenstate. Our results reveal fundamental properties of the entropy production in isolated quantum systems at late times.

Super-radiance reveals infinite-range dipole interactions through a nanofiber

Atoms interact with each other through the electromagnetic field, creating collective states that can radiate faster or slower than a single atom, i.e., super- and sub-radiance. When the field is confined to one dimension it enables infinite-range atom–atom interactions. Here we present the first report of infinite-range interactions between macroscopically separated atomic dipoles mediated by an optical waveguide. We use cold 87Rb atoms in the vicinity of a single-mode optical nanofiber (ONF) that coherently exchange evanescently coupled photons through the ONF mode. In particular, we observe super-radiance of a few atoms separated by hundreds of resonant wavelengths. The same platform allows us to measure sub-radiance, a rarely observed effect, presenting a unique tool for quantum optics. This result constitutes a proof of principle for collective behavior of macroscopically delocalized atomic states, a crucial element for new proposals in quantum information and many-body physics.

Changing optical band structure with single photons

Achieving strong interactions between individual photons enables a wide variety of exciting possibilities in quantum information science and many-body physics. Cold atoms interfaced with nanophotonic structures have emerged as a platform to realize novel forms of nonlinear interactions. In particular, when atoms are coupled to a photonic crystal waveguide, long-range atomic interactions can arise that are mediated by localized atom-photon bound states. We theoretically show that in such a system, the absorption of a single photon can change the band structure for a subsequent photon. This occurs because the first photon affects the atoms in the chain in an alternating fashion, thus leading to an effective period doubling of the system and a new optical band structure for the composite atom-nanophotonic system. We demonstrate how this mechanism can be engineered to realize a single-photon switch, where the first incoming photon switches the system from being highly transmissive to highly reflective, and analyze how signatures can be observed via non-classical correlations of the outgoing photon field.

Anomalous dispersion of microcavity trion-polaritons

A study of the strong coupling of different exciton species in two-dimensional molybdenum diselenide in a cavity uncovers the rich many-body physics and may lead to new devices. The strong coupling of excitons to optical cavities has provided new insights into cavity quantum electrodynamics as well as opportunities to engineer nanoscale light–matter interactions1,2,3,4,5,6. Here we study the interaction between out-of-equilibrium cavity photons and both neutral and negatively charged excitons, by embedding a single layer of the atomically thin semiconductor molybdenum diselenide in a monolithic optical cavity based on distributed Bragg reflectors. The interactions lead to multiple cavity polariton resonances and anomalous band inversion for the lower, trion-derived, polariton branch—the central result of the present work. Our theoretical analysis reveals that many-body effects in an out-of-equilibrium setting result in an effective level attraction between the exciton-polariton and trion-polariton accounting for the experimentally observed inverted trion-polariton dispersion. Our results suggest a pathway for studying interesting regimes in quantum many-body physics yielding possible new phases of quantum matter7,8,9,10,11 as well as fresh possibilities for polaritonic device architectures12,13,14,15.

Large exchange anisotropy in quasi-one-dimensional spin- 12 fluoride antiferromagnets with a d(z2)1 ground state

Hybrid density functional calculations are performed for a variety of systems containing d9 ions (Cu2+, Ag2+), and exhibiting quasi-one-dimensional magnetic properties. In particular we study fluorides containing these ions in a rarely encountered compressed octahedral coordination which forces the unpaired electron in the d(z2) orbital. We predict that such systems should exhibit magnetic anisotropies surpassing that of Sr2CuO3 - one of the best realizations of an one-dimensional system known to date. In particular we predict that the inter-chain coupling in the Ag2+ containing [AgF][BF4] should be nearly five orders of magnitude smaller than the intra-chain interaction. Our results indicate that quasi-one-dimensional spin-1/2 systems containing chains with spin sites in a d(z2)1 local ground state could constitute a versatile model for testing modern theories of quantum many-body physics in the solid state.

Projected regression method for solving Fredholm integral equations arising in the analytic continuation problem of quantum physics

We present a supervised machine learning approach to the inversion of Fredholm integrals of the first kind as they arise, for example, in the analytic continuation problem of quantum many-body physics. The approach provides a natural regularization for the ill-conditioned inverse of the Fredholm kernel, as well as an efficient and stable treatment of constraints. The key observation is that the stability of the forward problem permits the construction of a large database of outputs for physically meaningful inputs. Applying machine learning to this database generates a regression function of controlled complexity, which returns approximate solutions for previously unseen inputs; the approximate solutions are then projected onto the subspace of functions satisfying relevant constraints. Under standard error metrics the method performs as well or better than the Maximum Entropy method for low input noise and is substantially more robust to increased input noise. We suggest that the methodology will be similarly effective for other problems involving a formally ill-conditioned inversion of an integral operator, provided that the forward problem can be efficiently solved.

Squeezing in a nonlocal photon fluid

Quantum fluids of light are an emerging tool employed in quantum many-body physics. Their amazing properties and versatility allow using them in a wide variety of fields including gravitation, quantum information and simulation. However the implications of the quantum nature of light in the nonlinear optical propagation are still missing many features. We theoretically predict classical spontaneous squeezing of a photon fluid in a nonlocal nonlinear medium. By using the so called Gamow vectors, we show that the quadratures of a coherent state get squeezed and that a maximal squeezing power exists. Our analysis holds true for temporal and spatial optical propagation in highly nonlocal regime. These results open a new scenario in quantum photon fluids and may lead to novel applications in fields like metrology and analogues of quantum gravity.

ARC: An open-source library for calculating properties of alkali Rydberg atoms

We present an object-oriented Python library for the computation of properties of highly-excited Rydberg states of alkali atoms. These include single-body effects such as dipole matrix elements, excited-state lifetimes (radiative and black-body limited) and Stark maps of atoms in external electric fields, as well as two-atom interaction potentials accounting for dipole and quadrupole coupling effects valid at both long and short range for arbitrary placement of the atomic dipoles. The package is cross-referenced to precise measurements of atomic energy levels and features extensive documentation to facilitate rapid upgrade or expansion by users. This library has direct application in the field of quantum information and quantum optics which exploit the strong Rydberg dipolar interactions for two-qubit gates, robust atom-light interfaces and simulating quantum many-body physics, as well as the field of metrology using Rydberg atoms as precise microwave electrometers. Program summaryProgram Title: ARC: Alkali Rydberg CalculatorProgram Files doi:http://dx.doi.org/10.17632/hm5n8w628c.1Licensing provisions: BSD-3-ClauseProgramming language: Python 2.7 or 3.5, with C extensionExternal Routines: NumPy [1], SciPy [1], Matplotlib [2]Nature of problem: Calculating atomic properties of alkali atoms including lifetimes, energies, Stark shifts and dipole–dipole interaction strengths using matrix elements evaluated from radial wavefunctions.Solution method: Numerical integration of radial Schrödinger equation to obtain atomic wavefunctions, which are then used to evaluate dipole matrix elements. Properties are calculated using second order perturbation theory or exact diagonalisation of the interaction Hamiltonian, yielding results valid even at large external fields or small interatomic separation.Restrictions: External electric field fixed to be parallel to quantisation axis.Supplementary material: Detailed documentation (.html), and Jupyter notebook with examples and benchmarking runs (.html and .ipynb).[1] T.E. Oliphant, Comput. Sci. Eng. 9, 10 (2007). http://www.scipy.org/.[2] J.D. Hunter, Comput. Sci. Eng. 9, 90 (2007). http://matplotlib.org/.

Universal Critical Behaviours in Non-Hermitian Phase Transitions

Quantum phase transitions occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal critical behaviors for quantum phase transitions and quantum entanglement in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems. First, it bridges the non-analytic behavior of physical observable and no-analytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. Second, it predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being (1 − 1/p) with p being the number of coalesced states at the exceptional point. Third, it reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being (1 − 1/p). These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics.

Quantum Thermalization and the Expansion of Atomic Clouds

The ultimate consequence of quantum many-body physics is that even the air we breathe is governed by strictly unitary time evolution. The reason that we perceive it nonetheless as a completely classical high temperature gas is due to the incapacity of our measurement machines to keep track of the dense many-body entanglement of the gas molecules. The question thus arises whether there are instances where the quantum time evolution of a macroscopic system is qualitatively different from the equivalent classical system? Here we study this question through the expansion of noninteracting atomic clouds. While in many cases the full quantum dynamics is indeed indistinguishable from classical ballistic motion, we do find a notable exception. The subtle quantum correlations in a Bose gas approaching the condensation temperature appear to affect the expansion of the cloud, as if the system has turned into a diffusive collision-full classical system.

Towards Holography via Quantum Source-Channel Codes.

While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics, such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT) indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit nontrivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.

Single-molecule quantum dot as a Kondo simulator

Structural flexibility of molecule-based systems is key to realizing the novel functionalities. Tuning the structure in the atomic scale enables us to manipulate the quantum state in the molecule-based system. Here we present the reversible Hamiltonian manipulation in a single-molecule quantum dot consisting of an iron phthalocyanine molecule attached to an Au electrode and a scanning tunnelling microscope tip. We precisely controlled the position of Fe2+ ion in the molecular cage by using the tip, and tuned the Kondo coupling between the molecular spins and the Au electrode. Then, we realized the crossover between the strong-coupling Kondo regime and the weak-coupling regime governed by spin–orbit interaction in the molecule. The results open an avenue to simulate low-energy quantum many-body physics and quantum phase transition through the molecular flexibility.

Parity-time-symmetric quantum critical phenomena

Synthetic non-conservative systems with parity-time (PT) symmetric gain–loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii–Kosterlitz–Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics.

Entanglement from topology in Chern-Simons theory

The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary 3-manifolds with a fixed number of torus boundaries in both abelian U(1) and non-abelian SO(3) Chern-Simons theory. For the abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the nonabelian theory, we find a notion of "state universality", namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multi-boundary wormholes in AdS/CFT.

Quantum Entanglement in Neural Network States

Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states is recently becoming highly desirable in the applications of machine learning techniques to quantum many-body physics. Here, we study the quantum entanglement properties of neural-network states, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing efficiently quantum states with massive entanglement. We further examine generic RBM states with random weight parameters. We find that their averaged entanglement entropy obeys volume-law scaling and meantime strongly deviates from the Page-entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the unparalleled power of artificial neural networks in representing quantum many-body states, which paves a novel way to bridge computer science based machine learning techniques to outstanding quantum condensed matter physics problems.

Atomic physics: Quantum theory verified by experiment.

Systems of quantum objects can be characterized by the correlations between the objects. A technique that precisely measures even the most delicate of these correlations allows models of quantum systems to be tested. See Letter p.323 Ultracold gases of rubidium atoms on a quantum chip are well established analogue quantum simulators of quantum many-body physics. The system has been proposed to be described by a field theory called the sine-Gordon model, but verifying this requires direct measurement of higher-order correlation functions. Knowing all of the correlation functions of a system implies being able to characterize the system and solve the underlying quantum many-body problem. Here, the authors measure the higher-order correlation functions in an ultracold gas on a quantum chip from interference patterns, quantitatively confirming that it can indeed be described by a sine-Gordon model. Their methodology could in principle be applied to many types of quantum systems and hence will help to transform analogue quantum simulators into more quantitative and insightful tools.

Exact nonequilibrium dynamics of finite-temperature Tonks-Girardeau gases

Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly interacting bosons in one dimension in the Tonks-Girardeau regime of infinitely strong repulsive interactions. Using the Fredholm determinant approach and the Bose-Fermi mapping we show how the problem can be reduced to a single-particle basis, wherein the finite-temperature effects enter the solution via an effective "dressing" of the single-particle wavefunctions by the Fermi-Dirac occupation factors. We demonstrate the utility of our approach and its computational efficiency in two nontrivial out-of-equilibrium scenarios: collective breathing mode oscillations in a harmonic trap and collisional dynamics in the Newton's cradle setting involving real-time evolution in a periodic Bragg potential.

Designing exotic many-body states of atomic spin and motion in photonic crystals

Cold atoms coupled to photonic crystals constitute an exciting platform for exploring quantum many-body physics. For example, such systems offer the potential to realize strong photon-mediated forces between atoms, which depend on the atomic internal (spin) states, and where both the motional and spin degrees of freedom can exhibit long coherence times. An intriguing question then is whether exotic phases could arise, wherein crystalline or other spatial patterns and spin correlations are fundamentally tied together, an effect that is atypical in condensed matter systems. Here, we analyse one realistic model Hamiltonian in detail. We show that this previously unexplored system exhibits a rich phase diagram of emergent orders, including spatially dimerized spin-entangled pairs, a fluid of composite particles comprised of joint spin-phonon excitations, phonon-induced Néel ordering, and a fractional magnetization plateau associated with trimer formation.

Quantum Engineering of a Low-Entropy Gas of Heteronuclear Bosonic Molecules in an Optical Lattice

We demonstrate a generally applicable technique for mixing two-species quantum degenerate bosonic samples in the presence of an optical lattice, and we employ it to produce low-entropy samples of ultracold ^{87}Rb^{133}Cs Feshbach molecules with a lattice filling fraction exceeding 30%. Starting from two spatially separated Bose-Einstein condensates of Rb and Cs atoms, Rb-Cs atom pairs are efficiently produced by using the superfluid-to-Mott insulator quantum phase transition twice, first for the Cs sample, then for the Rb sample, after nulling the Rb-Cs interaction at a Feshbach resonance's zero crossing. We form molecules out of atom pairs and characterize the mixing process in terms of sample overlap and mixing speed. The dense and ultracold sample of more than 5000 RbCs molecules is an ideal starting point for experiments in the context of quantum many-body physics with long-range dipolar interactions.