DOCSLIB.ORG

Interplay of Quantum Phase Transition and Flat Band in Hybrid Lattices

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Interplay of Quantum Phase Transition and Flat Band in Hybrid Lattices PHYSICAL REVIEW RESEARCH 2, 033463 (2020) Interplay of quantum phase transition and flat band in hybrid lattices Gui-Lei Zhu ,1 Hamidreza Ramezani,2 Clive Emary ,3 Jin-Hua Gao,1 Ying Wu,1 and Xin-You Lü1,* 1School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China 2Department of Physics and Astronomy, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA 3Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle-Upon-Tyne NE1 7RU, United Kingdom (Received 8 October 2019; revised 18 June 2020; accepted 5 August 2020; published 22 September 2020) We establish a connection between quantum phase transitions (QPTs) and energy band theory in an extended Dicke-Hubbard lattice, where the periodical critical curves modulated by wave number k leadstorichequi- librium dynamics. Interestingly, the chiral-symmetry-protected flat band and the localization that it engenders exclusively occurs in the normal phase and disappears in the superradiant phase. This originates from the QPT induced simultaneous breaking up of the on-site resonance condition and off-site chiral symmetry of the system, which prohibits the destructive interference for obtaining a flat band. Our work offers an approach to identify different phases of the lattice via detecting the flat bands or simply the related localizations in a single cell, and, in turn, to control the appearance of flat bands by QPT. DOI: 10.1103/PhysRevResearch.2.033463 I. INTRODUCTION of light [23]. Recently, the flat bands have been observed in experiments with exciton-polariton condensates [24,25], The quantum phase transition (QPT), driven by quantum photonic lattices [26–29], and cold-atom lattices [30]. With fluctuations in many-body systems, is one of the most funda- an excellent and unique property, such a flat band is ro- mental and significant concepts in physics since it can offer bust against perturbations of system parameters, which opens the important resources for quantum metrology [1–3] and up the opportunity to detect phases of matter with strong quantum sensing [4–6]. For example, the generation of many- robustness. body entanglement through QPT enables precision metrology Here we established the connection between the flat band to reach the Heisenberg limit [7,8]. To apply QPT theory to and the QPT from the normal phase to the superradiant phase modern quantum technologies, a necessary task is to deter- in an extended Dicke-Hubbard lattice, i.e., a series of Dicke mine which phase the system is in. Traditionally, one needs models [31] coupled together through a set of atomless cavi- to detect the order parameters based on the ground states ties. Experimentally, this extended model can be implemented of the system [9], which is experimentally challenging in in hybrid superconducting circuits [32–38], in which a two- lattice systems where the complexity of the ground states in- level ensemble (e.g., NV center spins) is doped in every other creases exponentially with the size of the system. In addition, cavity [see Fig. 1(b)]. The superradiant QPT (a second-order the detecting precision is normally restricted by inevitable phase transition) was proposed in the single Dicke model experimental uncertainties and fabrication errors, e.g., small and occurs when increasing the atom-field coupling through perturbations. Hence, the development of a robust method to a critical point [39–51], which is associated with a sponta- precisely identify different phases of a quantum lattice system neously Z symmetry breaking. Extending to the periodic in the absence of ground-state detection is highly desired. 2 lattice, however, here we find that this critical point is replaced In the past decade and on a different subject, flat bands by the critical curves periodically modulated by wave num- (corresponding to a zero group velocity and an infinite ber k. The periodical boundaries of normal and superradiant effective mass) have been extensively studied in various phases intersect at some certain values of k. This predicts, condensed-matter contexts [10–16], on account of its potential in the lattice systems, a critical region between the normal applications in realizing the fractional quantum Hall effect and superradiant phases, where the first-order phase transi- in the absence of Landau levels [17–21], engineering strong tion and unstable phases alternatively appear in the different nonlinear correlations [22], and diffraction-free transmission range of k. The above connection allows us to identify different phases of the system via experimentally detectable energy bands (or *[email protected] the occupation localization in a single cell), and in turn, to control the occurrence of flat bands using QPT. Specifically, Published by the American Physical Society under the terms of the in the normal phase, a chiral-symmetry-protected flat band Creative Commons Attribution 4.0 International license. Further appears in the spectrum of the system, which features asym- distribution of this work must maintain attribution to the author(s) metric band structures originated from the counter-rotating and the published article’s title, journal citation, and DOI. interactions. This flat band disappears once the system enters 2643-1564/2020/2(3)/033463(9) 033463-1 Published by the American Physical Society GUI-LEI ZHU et al. PHYSICAL REVIEW RESEARCH 2, 033463 (2020) O = √1 eik·nO (O is an arbitrary annihilation operator (a) DM n N k k n and N is the number of unit cells). In the normal phase, the λ 1 H = / ψ† M ψ , ζ Hamiltonian is given by nor (k) 1 2 k nor nor (k) nor ψ = , , , , , T 2 where nor [akA akB bkA a−kA a−kB b−kA] and the su- perscript T denote a transpose operation. The coefficient is Spins Cavity A Cavity B collected into the matrix ⎛ ⎞ ωA f λ 0 f λ (b) C C C ⎜ ∗ ω ∗ ⎟ ⎜ f B 0 f 00⎟ ⎜ λ λ ⎟ M = ⎜ 0 00⎟, A B A B A B nor (k) (2) ⎜ 0 f λωA f λ⎟ ⎝ ∗ ∗ ⎠ f 00f ωB 0 C C C λ 00λ 0 =−ζ + FIG. 1. (a) Schematic illustration of a one-dimensional (1D) ex- where f [1 exp(ik)]. Here we have taken the lat- tice constant to be identical and a periodic boundary tended Dicke-Hubbard lattice, where the unit cell consists of a Dicke M model (spin ensemble collectively interacting with cavity A) coupled condition. The matrix nor (k) can be divided into the Mon = {ω ,ω ,,ω ,ω ,} to an atomless cavity B. Cavity A interacts with the spin ensemble on-site part nor (k) diag A B A B and off- Mint = M − Mon and cavity B with coupling strengths λ and ζ , respectively, forming site interaction part nor (k) nor (k) nor (k). In par- Mint two symmetric channels of the lattice, labeled 1 and 2. (b) The ticular, the interaction matrix nor (k) satisfies the chi- C†Mint C =−Mint C = implementation of the extended Dicke-Hubbard lattice in a hybrid ral symmetry with nor (k) nor (k), where superconducting circuit with capacitance coupling C and the ensem- diag{−1, 1, 1, −1, 1, 1}, and this symmetry is exact in the ble of spins in a diamond crystal. thermodynamic limit. The Hamiltonian Hnor (k) is bilinear in terms of bosonic operators, which can be analytically diagonalized. To analytically diagonalize the Hamiltonian into the superradiant phase. Physically, the superradiant QPT H (k), first we introduce an ancillary matrix D = τ M , makes both the excitation energy and an additional potential nor nor z nor where τ = diag{1, 1, 1, −1, −1, −1}. Second, we apply the of the spin ensemble interaction dependent, which breaks up z transformation matrix T into Hamiltonian H (k), where T the on-site resonant condition and off-site chiral symmetry nor simultaneously satisfies of the lattice, respectively. Either of them can destroy the destructive interference of the lattice and, finally, lead to the −1 Enor (k)0 disappearance of the flat band. T DnorT = , (3) 0 −Enor (−k) II. SUPERRADIANT PHASE TRANSITION T †τ T = τ IN 1D LATTICE SYSTEM and z z. Lastly, based on the above method and con- sidering = ωA = ωB = ω, the energy spectra of Hnor (k)are As illustrated in Fig. 1, we consider a 1D extended Dicke- Hubbard lattice implemented by a hybrid superconducting ⎧ ⎪ circuit, with the Hamiltonian ⎪ ω2 − ω ζ 2 + + λ2, ⎨⎪ 2 2 (1 cos k) Dicke Cavity ω, H = H + H + Hint, (1) Enor (k) = (4) nA nB ⎪ nA nB ⎩⎪ ω2 + 2ω 2ζ 2(1 + cos k) + λ2. where the subscript nA (nB) denotes the lattice site of cavity A Dicke † (B). The Dicke Hamiltonian is given by H = ωAa an + nA nA A Note that both the on-site resonance condition and off-site z √λ † + J + (a + an )(J + Jn ), where an is the annihi- nA N nA A nA A A chiral symmetry ultimately lead to a robust flat band lo- lation operator of cavity A mode, and Jz = (1/2) σ z , E k = ω nA N nA cated at nor ( ) in our model (detailed discussion is J± = σ ± are the collective operators of N spins. The shown below). Here the lowest excitation energy E l (λ, k) = nA N nA nor Cavity † Hamiltonian H = ω a a describes the bare cavity B. 2 2 2 nB B nB nB ω − 2ω 2ζ (1 + cos k) + λ indicates that our model is The nearest-neighbor cavities are coupled via an x-x interac- |ζ/ω| < / † † well defined when 1 4. Beyond this regime, the tion, Hint =−ζ , (a + an )(a + an ). nA nB nA A nB B Hamiltonian does not possess normalizable eigenfunctions To explore the phase transition in this extended Dicke- and has no obvious physical meaning for all values of other Hubbard lattice, we extend and modify the method in system parameters [52].
Load more

Recommended publications
  • Matter-Field Entanglement Within the Dicke Model
    Matter-Field Entanglement within the Dicke Model O. Casta~nos,R. L´opez-Pe~na,J. G. Hirsch, and E. Nahmad-Achar Instituto de Ciencias Nucleares, UNAM 2012{ Beauty in Physics: Theory and Experiment Matter-Field Entanglement Cocoyoc, 2012 Content The Dicke Hamiltonian Energy Surface of coherent states (CS) Symmetry adapted coherent states (SAS) Comparison variational vs Exact Results Fidelity Linear and von Neumann entropies Matter squeezing coefficient Conclusions 2012{ Beauty in Physics: Theory and Experiment Matter-Field Entanglement Cocoyoc, 2012 The Dicke Hamiltonian The Dicke model describes a cloud of cold atoms interacting with a one-mode electromagnetic field in an optical cavity [Dicke 1954] y γ y HD =a ^ a^ + !A^Jz + p a^ +a ^ ^J+ + ^J- : N Consider only the symmetric configuration of atoms i.e., N = 2j. The model presents a quantum phase transition when the p coupling constant, for N , takes the value γc = !A=2 [Hepp, Lieb 1973]. ! 1 2012{ Beauty in Physics: Theory and Experiment Matter-Field Entanglement Cocoyoc, 2012 Energy surface for CS The energy surface, or associated classical Hamilton function, is formed by means of the expectation value of the Hamiltonian with respect to a test state. We consider as test state the direct product of coherent states of the groups HW(1), for the electromagnetic part (Glauber 1963) and SU(2), for the atomic part (Arecchi et al 1972) , i.e., 2 +j e-jαj =2 αν 2j 1=2 p j+m jαi⊗jζi = j ζ jνi ⊗ jj; mi : 2 1 ν! j + m 1 + jζj ν=0 m=-j X X 2012{ Beauty in Physics: Theory and Experiment Matter-Field Entanglement Cocoyoc, 2012 Energy surface for CS The energy surface is given by H(α, ζ) ≡ hαj ⊗ hζjHDjαi ⊗ jζi 1 = p2 + q2 - j ! cos θ + 2pjγ q sin θ cos φ : 2 A We define 1 α = p (q + i p) ; 2 θ ζ = tan exp (i φ) ; 2 where (q; p) correspond to the expectation values of the quadratures of the electromagnetic field and (θ, φ) determine a point on the Bloch sphere.
    [Show full text]
  • Atom-Only Theories for U(1) Symmetric Cavity-QED Models
    PHYSICAL REVIEW RESEARCH 3, L032016 (2021) Letter Atom-only theories for U(1) symmetric cavity-QED models Roberta Palacino and Jonathan Keeling SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, United Kingdom (Received 26 November 2020; accepted 29 June 2021; published 19 July 2021) We consider a generalized Dicke model with U(1) symmetry, which can undergo a transition to a superradiant state that spontaneously breaks this symmetry. By exploiting the difference in timescale between atomic and cavity dynamics, one may eliminate the cavity dynamics, providing an atom-only theory. We show that the standard Redfield theory cannot describe the transition to the superradiant state, but including higher-order corrections does recover the transition. Our work reveals how the forms of effective theories must vary for models with continuous symmetry, and provides a template to develop effective theories of more complex models. DOI: 10.1103/PhysRevResearch.3.L032016 While phase transitions in equilibrium many-body sys- continuous symmetry breaking in extended multimode sys- tems have been extensively studied and are broadly un- tems allows one to explore the dispersion of the (complex) derstood [1,2], the critical behavior of driven-dissipative Goldstone modes [4,62] and their contribution to critical be- out-of-equilibrium systems [3–6] poses open questions. A havior. As noted above, theoretically modeling such systems central challenge in numerical exploration of such systems is challenging; one fruitful approach is to adiabatically elimi- is the exponential growth of Hilbert space dimension with nate fast degrees of freedom, providing an effective theory of problem size.
    [Show full text]
  • Experimentally Exploring the Dicke Phase Transition
    Diss. ETH No. 19943 Experimental Realization of the Dicke Quantum Phase Transition A dissertation submitted to the ETH Zurich¨ for the degree of Doctor of Sciences presented by Kristian Gotthold Baumann Dipl.-Phys., Technische Universit¨at Munchen,¨ Germany born 7.4.1983 in Leipzig, Germany citizen of Germany accepted on the recommendation of Prof. Dr. Tilman Esslinger, examiner Prof. Dr. Johann Blatter, co-examiner 2011 Zusammenfassung In dieser Arbeit wird die erste experimentelle Realisierung des Quantenphasenuberganges¨ im Dicke Modell vorgestellt. Wir betrachten die Quantenbewegung eines Bose-Einstein Konden- sates die an einen optischen Resonator gekoppelt ist. Konzeptionell ist der Phasenubergang¨ durch langreichweitige Wechselwirkungen induziert, die zum Entstehen eines selbstorgani- sierten suprasoliden Zustandes fuhren.¨ Der Quantenphasenubergang¨ im Dicke Modell wurde bereits 1973 vorhergesagt. Vor dieser Arbeit konnte dieser aber wegen grundlegenden und technologischen Grunden¨ experimentell nicht nachgewiesen werden. Durch die Verwendung von atomaren Impulszust¨anden konnten wir diese Herausforderung nun bew¨altigen. Die Impulszust¨ande werden durch Zweiphotonen- Uberg¨ ¨ange miteinander gekoppelt, wobei je ein Photon aus dem Resonator und ein Photon aus einer transversalen Lichtwelle gebraucht werden. Diese offene Implementierung des Di- cke Modells erlaubt es alle relevanten Parameter einzustellen und bietet eine einzigartige Detektionsmethode in Echtzeit. Wir zeigen in dieser Doktorarbeit, dass der Phasenubergang¨ von einem
    [Show full text]
  • Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-Integrable Dicke Model
    Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-integrable Dicke Model S. Lerma-Hernandez´ 1,2,a), J. Chavez-Carlos´ 2, M. A. Bastarrachea-Magnani3, B. Lopez-del-Carpio´ 2 and J. G. Hirsch2 1Facultad de F´ısica,Universidad Veracruzana, Circuito Aguirre Beltr´ans/n, C.P. 91000 Xalapa, Mexico 2Instituto de Ciencias Nucleares, Universidad Nacional Aut´onomade M´exico,Apdo. Postal 70-543, C.P. 04510 Cd. Mx., Mexico 3Physikalisches Institut, Albert-Ludwigs-Universitat Freiburg, Hermann-Herder-Str. 3, Freiburg, Germany, D-79104. a)Corresponding author: [email protected] Abstract. The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time t, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases. Introduction Simple models, originally proposed to study schematically quantum phenomena present in more realistic and elab- orated systems, have become experimentally feasible.
    [Show full text]
  • Arxiv:1807.04915V1 [Cond-Mat.Quant-Gas] 13 Jul 2018
    Spinor self-ordering of a quantum gas in a cavity Ronen M. Kroeze,1, 2, ∗ Yudan Guo,1, 2, ∗ Varun D. Vaidya,1, 2, 3 Jonathan Keeling,4 and Benjamin L. Lev1, 2, 3 1Department of Physics, Stanford University, Stanford, CA 94305 2E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305 3Department of Applied Physics, Stanford University, Stanford, CA 94305 4SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS UK (Dated: July 16, 2018) We observe the joint spin-spatial (spinor) self-organization of a two-component BEC strongly coupled to an optical cavity. This unusual nonequilibrium Hepp-Lieb-Dicke phase transition is driven by an off-resonant two-photon Raman transition formed from a classical pump field and the emergent quantum dynamical cavity field. This mediates a spinor-spinor interaction that, above a critical strength, simultaneously organizes opposite spinor states of the BEC on opposite checkerboard configurations of an emergent 2D lattice. The resulting spinor density-wave polariton condensate is observed by directly detecting the atomic spin and momentum state and by holographically reconstructing the phase of the emitted cavity field. The latter provides a direct measure of the spin state, and a spin-spatial domain wall is observed. The photon-mediated spin interactions demonstrated here may be engineered to create dynamical gauge fields and quantum spin glasses. The strong interaction between quantum matter or vice-versa) allowing the atoms to superradiantly scat- and light provided by cavity quantum electrodynamics ter photons into the cavity mode. The emergent coherent (QED) provides unique opportunities for exploring quan- field further orders the spins in a self-reinforcing man- tum many-body physics away from equilibrium [1{3].
    [Show full text]
  • Collective Dynamics of a Generalized Dicke Model
    Collective Dynamics of a Generalized Dicke Model J. Keeling, J. A. Mayoh, M. J. Bhaseen, B. D. Simons Harvard, January 2012 Funding: Jonathan Keeling Collective dynamics Harvard, January 2012 1 / 25 New relevance Superconducting qubits Quantum dots Nitrogen-vacancies in diamond Cavity κ κ Ultra-cold atoms Pump Pump Rydberg atoms Coupling many atoms to light Old question: What happens to radiation when many atoms interact “collectively” with light. Superradiance — dynamical and steady state. Jonathan Keeling Collective dynamics Harvard, January 2012 2 / 25 Cavity κ κ Pump Pump Coupling many atoms to light Old question: What happens to radiation when many atoms interact “collectively” with light. Superradiance — dynamical and steady state. New relevance Superconducting qubits Quantum dots Nitrogen-vacancies in diamond Ultra-cold atoms Rydberg atoms Jonathan Keeling Collective dynamics Harvard, January 2012 2 / 25 If jr − r j λ, use P S ! S dρ Γ i j i i = − S+S−ρ − S−ρS+ + ρS+S− Collective decay: dt 2 N/2 2 ΓN /2 z = j j = = /dt If S S N 2 initially: 〉 z 〉 S z z 2 0 〈 S d dhS i ΓN ΓN 〈 I / −Γ = sech2 t Γ dt 4 2 I=- -N/2 0 tD tD Problem: dipole interactions dephase. [Friedberg et al, Phys. Lett. 1972] Dicke effect: Enhanced emission X y − −ik·ri Hint = gk k Si e + H.c. k;i Jonathan Keeling Collective dynamics Harvard, January 2012 3 / 25 N/2 2 ΓN /2 z = j j = = /dt If S S N 2 initially: 〉 z 〉 S z z 2 0 〈 S d dhS i ΓN ΓN 〈 I / −Γ = sech2 t Γ dt 4 2 I=- -N/2 0 tD tD Problem: dipole interactions dephase.
    [Show full text]
  • Two-Level Systems Coupled to Oscillators
    Chapter 35. Two-level systems and oscillators Two-level systems coupled to oscillators RLE Group Energy Production and Conversion Group Project Staff Peter L. Hagelstein and Irfan Chaudhary Introduction Basic physical mechanisms that are complicated can often be studied with the aid of simple quantum mechanical models that exhibit the effects of interest. We have been interested in energy exchange between two-level systems and an oscillator under conditions where the two- level system energy is much greater than the oscillator energy. This problem first became of interest in quantum mechanics in the course of early NMR studies by Bloch and Siegert [1]. A strong applied magnetic field causes a splitting of spin levels, creating a two-level system in the case of a spin ½ nucleus. A dynamical transverse field causes transitions between the upper and lower levels of the two-level system. Early work on this problem was done using the Rabi Hamiltonian, in which the oscillator appears in the problem as a time-dependent interaction potential [1,2]. In the mid 1970s, Cohen-Tannoudji and colleagues introduced the spin-boson model, in which a quantum model is used for the oscillator [3]. The spin-boson model in recent years has been used to model electromagnetic interactions between atomic or molecular systems and radiation fields, as well as serving as a workhorse model for testing new kinds of approximations or formulations. By now, there are hundreds of papers on spin-boson and related models, and the interest in such models as basic physical models is only increasing. We have been interested in the spin-boson model and the closely related Dicke model (which generalizes the spin-boson model to include many identical two-level systems) in the multiphoton regime, in order to focus on the coherent exchange of many small oscillator quanta for a single large two-level system quantum.
    [Show full text]
  • Characterizing the Dynamical Phase Diagram of the Dicke Model Via Classical and Quantum Probes
    PHYSICAL REVIEW RESEARCH 3, L022020 (2021) Letter Characterizing the dynamical phase diagram of the Dicke model via classical and quantum probes R. J. Lewis-Swan ,1,2 S. R. Muleady ,3,4,* D. Barberena ,3,4,* J. J. Bollinger ,5 and A. M. Rey 3,4 1Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA 2Center for Quantum Research and Technology, The University of Oklahoma, Norman, Oklahoma 73019, USA 3JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA 4Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA 5National Institute of Standards and Technology, Boulder, Colorado 80305, USA (Received 8 February 2021; accepted 11 May 2021; published 4 June 2021) We theoretically study the dynamical phase diagram of the Dicke model in both classical and quantum limits using large, experimentally relevant system sizes. Our analysis elucidates that the model features dynamical critical points that are strongly influenced by features of chaos and emergent integrability in the model. Moreover, our numerical calculations demonstrate that mean-field features of the dynamics remain valid in the exact quantum dynamics, but we also find that in regimes where quantum effects dominate signatures of the dynamical phases and chaos can persist in purely quantum metrics such as entanglement and correlations. Our predictions can be verified in current quantum simulators of the Dicke model including arrays of trapped ions. DOI: 10.1103/PhysRevResearch.3.L022020 Introduction. Advances in atomic, molecular, and optical freedom such that the model remains amenable to analytic and (AMO) quantum simulators are driving a surge in the investi- numerical treatments.
    [Show full text]
  • Exact Solutions of an Extended Dicke Model
    Physics Letters A 341 (2005) 94–100 www.elsevier.com/locate/pla Exact solutions of an extended Dicke model Feng Pan a,b,∗,TaoWanga,JingPana, Yong-Fan Li a, J.P. Draayer b a Department of Physics, Liaoning Normal University, Dalian 116029, PR China b Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA Received 1 February 2005; received in revised form 19 April 2005; accepted 4 May 2005 Available online 11 May 2005 Communicated by P.R. Holland Abstract Exact solutions of the Dicke Hamiltonian plus a dipole–dipole interaction among N two-level atoms are derived based on an algebraic Bethe ansatz. As an example application, the role of the dipole–dipole interaction in ground-state-atom condensates of a system is explored. 2005 Elsevier B.V. All rights reserved. PACS: 42.50.Ct; 42.50.Dv; 42.50.Hz; 42.50.Fx Keywords: Extended Dicke model; Dipole–dipole interaction; Exact solution A description of the interaction of a collection of atoms with a radiation field is a model problem in matter–field interaction phenomena that is of interest in many areas of physics. But because it is generally impossible to obtain exact solutions for this problem, approximations are normally adopted. The most common approximation assumes that the radiation field is quasi-monochromatic and the atoms are identical with no direct interactions between or among themselves. The Dicke model [1,2], which is the natural consequence of such an assumption, describes the interaction of N identical two-level atoms with a single-mode field in a perfect cavity.
    [Show full text]
  • Dicke-Type Phase Transition in a Spin-Orbit-Coupled Bose&Ndash
    ARTICLE Received 16 Jan 2014 | Accepted 30 Apr 2014 | Published 4 Jun 2014 DOI: 10.1038/ncomms5023 Dicke-type phase transition in a spin-orbit-coupled Bose–Einstein condensate Chris Hamner1, Chunlei Qu2, Yongping Zhang1,3, JiaJia Chang1, Ming Gong2,4, Chuanwei Zhang1,2 & Peter Engels1 Spin-orbit-coupled Bose–Einstein condensates (BECs) provide a powerful tool to investigate interesting gauge field-related phenomena. Here we study the ground state properties of such a system and show that it can be mapped to the well-known Dicke model in quantum optics, which describes the interactions between an ensemble of atoms and an optical field. A central prediction of the Dicke model is a quantum phase transition between a superradiant phase and a normal phase. We detect this transition in a spin-orbit-coupled BEC by measuring various physical quantities across the phase transition. These quantities include the spin polarization, the relative occupation of the nearly degenerate single-particle states, the quantity analogous to the photon field occupation and the period of a collective oscillation (quadrupole mode). The applicability of the Dicke model to spin-orbit-coupled BECs may lead to interesting applications in quantum optics and quantum information science. 1 Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA. 2 Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA. 3 Quantum System Unit, Okinawa Institute of Science and Technology, Okinawa 904-0495, Japan. 4 Department of Physics and Center of Coherence, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China.
    [Show full text]
  • Mesoscopic Entanglement Induced by Spontaneous Emission in Solid-State Quantum Optics
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE weekprovided ending by Sussex Research Online PRL 110, 080502 (2013) PHYSICAL REVIEW LETTERS 22 FEBRUARY 2013 Mesoscopic Entanglement Induced by Spontaneous Emission in Solid-State Quantum Optics Alejandro Gonza´lez-Tudela1 and Diego Porras2 1Departamento de Fı´sica Teo´rica de la Materia Condensada, Universidad Autonoma de Madrid, 28040 Madrid, Spain 2Departamento de Fı´sica Teo´rica I, Universidad Complutense, 28040 Madrid, Spain (Received 21 September 2012; revised manuscript received 29 November 2012; published 20 February 2013) Implementations of solid-state quantum optics provide us with devices where qubits are placed at fixed positions in photonic or plasmonic one-dimensional waveguides. We show that solely by controlling the position of the qubits and with the help of a coherent driving, collective spontaneous decay may be engineered to yield an entangled mesoscopic steady state. Our scheme relies on the realization of pure superradiant Dicke models by a destructive interference that cancels dipole-dipole interactions in one dimension. DOI: 10.1103/PhysRevLett.110.080502 PACS numbers: 03.67.Bg, 03.67.Ac, 37.10.Ty, 37.10.Vz The study of atoms coupled to the electromagnetic (EM) distance. Adding a classical drive to the pure Dicke model field confined in cavities or optical waveguides has played we obtain a dissipative system with a phase diagram of a central role in the fields of quantum optics and atomic steady states showing mesoscopic spin squeezing and physics. In recent years the basics of that physical system entanglement. This model has been theoretically investi- have been realized with artificially designed atoms in gated in the past [25–27], but experimental realizations are solid-state setups.
    [Show full text]
  • Non-Equilibrium Phase Transition in a Spin-1 Dicke Model
    Non-Equilibrium Phase Transition in a Spin-1 Dicke Model Zhang Zhiqiang1;2, Chern Hui Lee1;2, Ravi Kumar1;2, K. J. Arnold1;2, Stuart J. Masson3, A. S. Parkins3 and M. D. Barrett1;2 1Center for Quantum Technologies, 3 Science Drive 2, 117543, Singapore 2Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore 3Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand Abstract We realize a spin-1 Dicke model using magnetic sub-levels of the lowest F = 1 hyperfine level of 87Rb atoms confined to a high finesse cavity. We study this system under conditions of imbalanced driving, which is predicted to have a rich phase diagram of nonequilibrium phases and phase transitions. We observe both super-radiant and oscillatory phases from the cavity output spectra as predicted by theory. Exploring the system over a wide range of parameters, we obtain the boundaries between the normal, super-radiant and the oscillatory phases, and compare with a theoretical model. Keywords: Quantum physics, Cavity QED, Superradiance 1. Introduction The study of atom-light interactions has been an important area of research due to its importance in understanding of fundamental physics, especially quantum optics, and potential technological applications, such as quantum computation [1], the quantum internet [2], atomic clocks [3], arXiv:1612.06534v1 [quant-ph] 20 Dec 2016 and superradiant lasers [4]. A significant amount of effort has been devoted to study coherent control of atoms by strong atom-photon interactions using various systems including optical cavities [5], atom chips [6], and structured optical waveguides [7].
    [Show full text]