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Europhysics Letters (EPL)

Interaction-induced topological quantum interference in an extended Dicke model

Gang Chen, Zheng‐Yuan Xue, L. F. Wei, J.-Q. Liang

Published May 1, 2009• 3 citations
Publisher

Abstract

In this paper we predict a topological quantum interference effect in an extended Dicke model with controllable long-range atom-atom interactions by means of coherent-state path integral. Due to the intrinsic competition between the atom-atom interactions and atom-field coupling, an interesting topological interference of the instanton and anti-instanton tunneling paths could occur. As a consequence, this model only with a few odd-number atoms has a twofold absolute degenerate ground-state subspace with a large energy gap, which becomes larger with the increasing of the system size. Therefore, the collective decoherence arising from noise in the external control parameters could be effectively suppressed in terms of adiabatic process between this absolute degenerate ground-state subspace associated with a finite energy gap.

DOI
10.1209/0295-5075/86/44002

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In this paper we predict a topological quantum interference effect in an extended Dicke model with controllable long-range atom-atom interactions by means of coherent-state path integral. Due to the intrinsic competition between the atom-atom interactions and atom-field coupling, an interesting topological interference of the instanton and anti-instanton tunneling paths could occur. As a consequence, this model only with a few odd-number atoms has a twofold absolute degenerate ground-state subspace with a large energy gap, which becomes larger with the increasing of the system size. Therefore, the collective decoherence arising from noise in the external control parameters could be effectively suppressed in terms of adiabatic process between this absolute degenerate ground-state subspace associated with a finite energy gap.
The Dicke model describes NNN two-level atoms interacting with a single-mode bosonic field and exhibits a second-order phase transition from the normal to the superradiant phase. The energy levels are not degenerate in the normal phase but have degeneracy in the superradiant phase, where quantum tunneling occurs. By means of the Born-Oppenheimer approximation and the instanton method in quantum field theory, the tunneling splitting, inversely proportional to the tunneling rate for the adiabatic Dicke model, in the superradiant phase can be evaluated explicitly. It is shown that the tunneling splitting vanishes as $\mathrm{exp}(\ensuremath{-}N)$ for large NNN, whereas for small NNN it disappears as N∕exp(N)\sqrt{N}∕\mathrm{exp}(N)N​∕exp(N). The dependence of the tunneling splitting on the relevant parameters, especially on the atom-field coupling strength, is also discussed.
Abstract In this article, we use the spin coherent state transformation and the ground state variational method to theoretically calculate the ground function. In order to consider the influence of the atom-atom interaction on the extended Dicke model’s ground state properties, the mean photon number, the scaled atomic population and the average ground energy are displayed. Using the self-consistent field theory to solve the atom-atom interaction, we discover the system undergoes a first-order quantum phase transition from the normal phase to the superradiant phase, but a famous Dicke-type second-order quantum phase transition without the atom-atom interaction. Meanwhile, the atom-atom interaction makes the phase transition point shift to the lower atom-photon collective coupling strength.
Quantum interference and coherence effects in the interaction of atoms with the quantized electromagnetic field are investigated theoretically. A general master equation for the description of atom-field interactions is introduced. The interplay of the concepts of complementarity and interference in the time-energy domain are studied on the basis of the fluorescence light emitted by a single laser-driven atom, where the coherence of spontaneous processes gives rise to quantum interference in the spectrum of resonance fluorescence. The vacuum-induced dipole-dipole interaction in pairs of multi-level atoms is analyzed. It is shown that the interaction between orthogonal transition dipole moments of different atoms does not only influence the system dynamics crucially, but implies that the few-level approximation in general cannot be applied to near-degenerate Zeeman sublevels of the atomic level scheme. Potential applications of dipole-dipole interacting multi-level atoms for the implementation of decoherence-free subspaces and the generation of entanglement between atomic states are examined. The generation of an entangled state of the radiation field with a macroscopic number of photons is discussed on the basis of a single-atom laser.
Ultracold atomic quantum systems offer an unprecedentedly powerful platform for exploring interacting symmetry-protected topological phases. Here, we show that their characteristic control over temperature provides a resource for engineering effective topological regimes with no zero-temperature counterpart. Employing finite-temperature matrix-product-state calculations, we investigate experimentally accessible Hamiltonians - the interacting bosonic Su-Schrieffer-Heeger and spin-1 XXZ chains - that host a topological phase at zero temperature, as well as a fermionic dipolar ladder model whose ground state exhibits no topological order. By tracking complementary topological markers, we identify an intriguing mechanism rooted in the structure of the zero-temperature phase diagrams: in finite-size systems, excitation gaps with different magnitudes define an intermediate-temperature window where the correlations associated with the lower gap are suppressed, while those protected by the larger gap persist. This enables the emergence of effective finite-temperature regimes exhibiting topological features that are either absent or qualitatively different from those at zero temperature. Our results establish a novel route toward exploring effective topological phases in ultracold atomic quantum systems.
We investigate the role of interatomic interactions when a Bose gas, in a double-well potential with a finite tunneling probability (a ‘Bose–Josephson junction’), is exposed to external noise. We examine the rate of decoherence of a system initially in its ground state with equal probability amplitudes in both sites. The noise may induce two kinds of effects: firstly, random shifts in the relative phase or number difference between the two wells and secondly, loss of atoms from the trap. The effects of induced phase fluctuations are mitigated by atom–atom interactions and tunneling, such that the dephasing rate may be suppressed by half its single-atom value. Random fluctuations may also be induced in the population difference between the wells, in which case atom–atom interactions considerably enhance the decoherence rate. A similar scenario is predicted for the case of atom loss, even if the loss rates from the two sites are equal. We find that if the initial state is number-squeezed due to interactions, then the loss process induces population fluctuations that reduce the coherence across the junction. We examine the parameters relevant for these effects in a typical atom chip device, using a simple model of the trapping potential, experimental data, and the theory of magnetic field fluctuations near metallic conductors. These results provide a framework for mapping the dynamical range of barriers engineered for specific applications and set the stage for more complex atom circuits (‘atomtronics’).
We introduce an extended Dicke model with controllable long-range atom-atom interaction to simulate topologically ordered states and achieve decoherence-protected qubits. We illustrate our idea in an experimentally feasible circuit quantum electrodynamics scenario. Due to the intrinsic competition with the atom-field coupling strength, we first demonstrate that this atom-atom interaction can exhibit a novel topological quantum interference effect arising from the instanton and anti-instanton tunneling paths. As a consequence, this proposed model only with a few odd-number of atoms has a two-fold absolute degenerate ground-subspace with a large energy gap, which can become larger with the increasing of the system-size. It may also support the excitation of anyonic statistics, and thus can be regarded as a possible candidate for processing topological quantum memory.