Abstract:
We predict that an atomic Bose-Einstein condensate strongly coupled to an intracavity optical lattice can undergo resonant tunneling and directed transport when a constant and uniform bias force is applied. The bias force induces Bloch oscillations, causing amplitude and phase modulation of the lattice which resonantly modifies the site-to-site tunneling. For the right choice of parameters a net atomic current is generated. The transport velocity can be oriented oppositely to the bias force, with its amplitude and direction controlled by the detuning between the pump laser and the cavity. The transport can also be enhanced through imbalanced pumping of the two counter-propagating running wave cavity modes. Our results add to the cold atoms quantum simulation toolbox, with implications for quantum sensing and metrology.
Ref: J. Goldwin, B. Prasanna Venkatesh, D. H. J. O'Dell, Phys. Rev. Lett. 113, 073003 (2014)
Abstract:
The photo-excited dynamics in strongly correlated electron systems is one of the attractive subjects in condensed matter physics. It is believed that the competition of orders and multi-instability play important roles to the photo-induced phase transition.
As examples of systems with competition of orders, we consider the frustrated charge ordered (CO) systems. We calculate the real-time dynamics in the spinless Vt fermion model on a triangular lattice using the exact-diagonalization. We find the dynamics varies widely in response to the CO patterns before photo-excitations. We also examine the dynamics in lattice-coupled CO systems
Abstract:
Boltzmann's transport equation determines the dynamical flow of the dissipative fluid. The system has the velocity
field as the mechanical variables. Some classical flow,
such as Navier-Stokes flow, usually dominates. The present interest is on the statistical fluctuation around
the classical flow. The fluctuation comes from the micro movement of the constituent particles of the flow.
Generally the velocity field statistically fluctuates.
We introduce the fluctuation effect by the use of Feynman's path integral.
Formally it is the same as the ordinary quantization, but we do not use Planck constant. Instead of it,
we use the characteristic scale of the flow. We do not
use the time variable 't', but use the step number 'n'.
Discrete Morse flow method tells us the recursion relation
between the velocity distribution at n-step and that at
(n-1)-step. The relation determines the time development
of the system. We apply this approach to 1D non-equilibrium
model and present numerical simulation data.
(Related reference: arXiv:1303.6616 "Velocity-Field, Boltzmann's Transport ...")
Abstract:
We present the formulation for nonequilibrium processes of the cold atomic gas systems, using nonequilibrium Thermo Field Dynamics (TFD), which is a real-time canonical formalism of quantum field theory for thermal situations [H. Umezawa, “Advanced Field Theory -Micro, Macro, and Thermal Physics” (AIP, New York, 1993)]. Because the quasiparticle picture can be defined explicitly in nonequilibrium TFD, we can in principle deal with condensate systems with time-dependent order parameter. Remarkably in nonequilibrium TFD, one derives the quantum transport equation for the cold atomic gas systems from the renormalization condition which is a fundamental concept of quntum field theory. The quantum transport equation, thus derived, is non-Markovian [Y. Nakamura, et al., Ann. Phys. 325 (2010) 426; Y. Nakamura, et al., ivid. 326 (2011) 1070; Y. Nakamura, et al., ivid. 331 (2013) 51]. We will show some properties of the transport equation and attempt to solve it numerically.
Abstract:
Recent femtosecond pump-probe experiments on Mott-Hubbard insulators reveal charge dynamics on several scales, varying from faster relaxation in femtosecond range to slower recombination in picosecond range. Mechanisms explainig the measured time-scales depend on the dimensionality of the system, and especially on the degrees of freedom that are available to take the excessive energy of excited charged particles, either in relaxation or recombination process. Firstly, charge relaxation with a spin-lattice polaron formation after a quantum quench that simulates absorption of the pump-pulse will be adressed, showing a two-stage dynamics in the presence of spin and lattice degrees of freedom that appear to be independent in the first, and intertwined in the second stage, raising also the question of fast thermalisation of particle. As the subsequent process, we will present and contrast mechanisms for the recombination of charged particles in one- and two-dimensional Mott-Hubbard insulators, as relevant for effectively one-dimensional organic salts and two-dimensional cuprates, claiming that in the former energy is transmitted to molecular vibrations whereas in the latter to the spin excitations, supported by calculated recombination rates reproducing the measurements.
References:
Z. Lenarcic and P. Prelovsek, PRL 111, 016401 (2013)
Z. Lenarcic and P. Prelovsek, arXiv 1409.2347 (2014)
J. Kogoj et al, arXiv 1402.6104 (2014)
Abstract:
Recently, heavy fermion systems in quasicrystals is attracting attention after quantum critical phenomena has been found in the quasicrystal[1].
We consider the one-dimensional quasiperiodic Anderson model, which has quasiperiodically ordered impurities.
To treat the correlation effect precisely, we use density matrix renormalization group(DMRG) method, and we analyze magnetic properties of this model.
Moreover, we consider the relation between quasiperiodic Anderson model and quasiperiodic Bose-Hubbard model, where we have discussed the topological properties of the incommensurate charge density wave phase in our previous work[2].
[1] K. Deguchi et al., Nature Materials 11, 1013 (2012).
[2] F. Matsuda, M. Tezuka, and N. Kawakami, J. Phys. Soc. Jpn. 83, 083707 (2014).
Abstract:
The non-equilibrium properties of strongly correlated systems are recently attracting much interest. In many materials, it is expected that phonon degrees of freedoms play an important role in the dynamics because of a significant coupling between electrons and phonons. Indeed, oscillation originating from phonons is observed in pump-probe experiments [1]. However, theoretically, it is still not well understood how the phonon dynamics affects the relaxation process of an electron-phonon system and how the latter is different from the relaxation of a purely electronic system such as the Hubbard model.
In our study[2], we address these points by investigating the relaxation process in the simplest model for electron-phonon systems, i.e. the Holstein model, after a sudden change in the electron-phonon coupling. Here, we employ the non-equilibrium dynamical mean-field theory [3] and the self-consistent Migdal approximation as an impurity solver. We have revealed that there occurs a crossover in the thermalization process in the coupling regime prior to bipolaron formation but with significant electron correlation. The first type of the relaxation is reminiscent of the prethermalization phenomenon in the Hubbard model, where local quantities approach their thermal value faster than the momentum distribution of the electrons. In the second type of relaxation, the momentum distribution quickly approaches the thermal distribution for some appropriately defined effective temperature, but it continues to oscillate because of the slow damping of the phonons. We also discuss the relation between these two relaxation processes and the self-energies of the electrons and phonons. In addition, importance of phonon dynamics is endorsed by comparing the present result with the Hartree-Fock approximation that neglects phonon dynamics, where the relaxation processes turn out to be totally different.
[1] L. Perfetti et al, PRL 97, 067402 (2006); S. L. Johnson et al, PRL,102, 175503 (2009).
[2] Y. Murakami, P. Werner, N. Tsuji and H. Aoki, arXiv:1407.8288.
[3] J. K. Freericks et al, PRL, 97, 266408 (2008); H. Aoki et al, RMP, 86, 779 (2014).
Abstract:
Metal-insulator transition and Kondo effect are both one of the central concepts in strongly correlated systems. In this presentation, we investigate the cooperation of these concepts in time-dependent, non-equilibrium situations, and propose a new phenomenon, dubbed "photo-induced Kondo effect". Motivated by recent progress in ultracold atomic physics using alkaline-earth species[1], we consider a two-orbital system consisting of a Mott insulator and itinerant free fermions, and apply an external ac field which drives the system into non-equilibrium states. The ac field induces hybridization between the two orbitals, and thus dissolves the Mott insulator in the free fermionic "bath" degrees of freedom, which is reminiscent of Kondo effect in lattice systems. We investigate the dynamical melting phenomena of the Mott insulator and the formation of heavy fermions due to Kondo effect, using the Keldysh Green function method[2] and slave-boson representation.
[1] A. V. Gorshkov, M. Hermele, V. Gurarie, C. Xu, P. S. Julienne, J. Ye, P. Zoller, E. Demler, M. D. Lukin, and A. M. Rey: Nat. Phys. 6, 289 (2010).
[2] H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, and P. Werner: Rev. Mod. Phys. 86, 779 (2014).
Abstract:
In the recent years, nonequilibrium quantum systems have become a major subject of study in condensed matter [1]. One of the most important questions is the equilibration and thermalizatiton in isolated quantum systems. Quantum quenches, abrupt changes of the Hamiltonian of a system, offer simple protocols to tackle such problems.
In the present work we study a flux quench in the spin-$1/2$ Heisenberg XXZ chain. The flux quench is a quantum quench where the flux \(\phi\) piercing the XXZ chain is turned off at \(t=0\) suddenly. If we formulate the XXZ chain as a spinless fermion model, the flux \(\phi\) corresponds to a vector potential on each bond and this flux quench can be viewed as imposing pulse (delta function) of electric field. Therefore the flux quench generates some particle (or spin) current at time \(t=0\). In [2], the flux quench was studied to illustrate the breakdown of the relaxation towards the generalized Gibbs ensemble in integrable systems.
Here we focus on the time evolution of the spin current after the quench and calculate it numerically by the infinite time-evolving block decimation (iTEBD) method. We find that the current oscillates and decays after the quench and that the frequency of the oscillations and the rate of decay depend strongly on the anisotropy parameter $\Delta$ of XXZ chain. We discuss the nature of the dynamics and relaxation of the current and compare it with the results from linear response theory.
[1] A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011).
[2] M. Mierzejewski, P. Prelovsek and T. Prosen, Phys. Rev. Lett. 113, 020602 (2014).
Abstract:
Recently non-equilibrium dynamics of cold atom systems has been enthusiastically targeted, because cold atom systems are ideal as isolated quantum systems configured in laboratory, whose parameters can be modified dynamically [1]. While the dynamics of quantum quench has been explored by suddenly changing the trap potential and the interaction, dynamics induced by a gradual change of parameters in real time has a lot more to be investigated.
We study typical drag dynamics of several fermions (a cluster) in a fermion cloud in one-dimensional continuous systems, with particular emphasis on the non-trivial quantum many-body effects in systems whose parameters change gradually in real time. We adopt the Fermi-Hubbard model and the time-dependent density matrix renormalization group method [2] to calculate the drag force on a trapped fermion cluster as it is emerged in and interacts with a cloud of another species of fermions. A non-trivial peak in the resistance force is observed in the large cloud density region, and it is suggested that some momentum redistribution processes have a crucial role in the excitation process [3]. We propose a simplified model which explains the detail of the excitation process and also the origin of the resistance peak. This model emphasizes the difference between the full-quantum calculation and the semiclassical calculation, which is the quantum effects, in slow dynamics of many-body systems bound in a fermion cloud.
References:
[1] A. Sommer, M. Ku, G. Roati and M.W. Zwierlein, Nature 472, 201 (2011).
[2] S. R. White and A. E. Feiguin, Phys. Rev. Lett. 93, 076401 (2004).
[3] J. Ozaki, M. Tezuka and N. Kawakami, arXiv:1402.6486.
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Abstract:
Several species of atoms have multiple low-lying hyperfine states in cold atomic systems. By loading these atoms into optical lattices, one can realize the multicomponent Fermi systems. Recently, six-component Fermi systems were experimentally realized[1], and have attracted much interest.
These backgrounds motivate us to study quantum condensed phases and quantum phase transitions which can be observed in attractively interacting multicomponent Fermi systems with disorder at finite temperatures. For this purpose, we apply the determinant Quantum Monte Carlo scheme[2] to the multicomponent Hubbard model with attractive interaction and disorder, and calculate the pair-correlation function and the charge-correlation function. In this poster presentation, we will show the results of these two functions and discuss how the fluctuations of pair-correlation and charge-correlation lead to the pseudo-gap formation at finite temperatures.
[1] S. Taie, R. Yamazaki, S. Sugawa, and Y Takahashi, Nat. Phys. 8, 825 (2012).
[2] S. R. White, D. J. Scalapino, R. L. Sugar, E. Y. Loh, J. E. Gubernatis, and R. T. Scalettar, Phys. Rev. B 40, 506 (1989).
Abstract:
We extend the bosonic dynamical mean-field formalism to nonequilibrium situations and test it in combination with a Nambu real-time strong coupling perturbative impurity solver [1]. The formalism correctly describes the Mott insulating, superfluid and normal phases, and captures damping and thermalization at finite temperatures, in contrast to other real-time approaches.
As a first application we study bosonic cold-atoms in an optical lattice using the Bose-Hubbard model. Already in equilibrium the spectral function display non-trivial features beyond the RPA treatment [2], and the real-time implementation gives a considerably improved resolution compared to analytical continuation [3].
We drive the system out of equilibrium buy quenching the interaction, mimicking the seminal cold-atom experiment of Greiner et al. [4]. Starting from both the normal and superfluid phase, we map out non-equilibrium phase diagrams which identify the different dynamical regimes. A multitude of behaviors are observed, including rapid thermalization and trapping in meta-stable normal and superfluid states. Depending on parameters, the condensate displays long lived or strongly damped amplitude oscillations, and in some cases even a transient enhancement (nonequilibrium Bose condensation [5]).
Nonequilibrium bosonic dynamical mean-field theory can be straightforwardly extended to enable the study of the nonequilibrium properties of bosonic multi-component systems [6] and Bose-Fermi mixtures [7].
1. H. U. R. Strand, M. Eckstein, P. Werner, arXiv:1405.6941 (2014)
2. C. Menotti, N. Trivedi, PRB 77, 235120 (2008)
3. K. Byczuk, D. Vollhardt, PRB 77, 235106 (2008)
4. M. Greiner, O. Mandel, T. W. Hansch, I. Bloch, Nature 419, 51 (2002)
5. J. Berges, D. Sexty, PRL 108, 161601 (2012)
6. A. Hubener, M. Snoek, W. Hofstetter, PRB 80, 245109 (2009)
7. P. Anders, P. Werner, M. Troyer, M. Sigrist, L. Pollet, PRL 109, 206401 (2012)
Abstract:
We investigate superfluid of three-component repulsive fermionic atoms in optical lattices. Using a dynamical mean field theory we show that when two of the three repulsions are much stronger than the other, a superfluid state appears at and close to half filling [1]. In this superfluid weakly interacting atoms form Cooper pairs, while atoms with the rest color remain a Fermi liquid. We further investigate pairing symmetry using an Eliashberg equation. We evaluate the effective pairing interaction by collecting RPA-type diagrams and ladder diagrams. We find that when two of the three repulsions are much stronger than the other, pairing symmetry is an extended s wave. As the difference in three repulsions is reduced, pairing symmetry changes into a nodal s wave and then into d waves. This change is caused by the change in dominant quantum fluctuations. We expect 6Li atoms and \({}^{171}\)Yb-\({}^{173}\)Yb mixtures to be possible candidates for observing these superfluid states.
[1] K. Inaba and S. Suga, Phys. Rev. Lett. 108, 255301 (2012).
Abstract:
We study the boundary states of trapped two-dimensional bosonic Mott states in optical lattices, by performing quantum Monte Carlo simulation. From the temperature dependence of local superfluid density and correlation functions, we find a characteristic temperature \(T^*\). Below \(T^*\), the edge region of the Mott state possesses a finite superfluid density and the one-particle equal-time Green function in the edge region decays in a almost power-law fashion. This suggests that the an undesired (normal) gapless mode is generally observed in trapped Bose Mott states regardless of the existence of an intrinsic gapless edge mode in topological Mott states.
Abstract:
We investigate the non-equilibrium dynamics following a quantum quench in a single-species superfluid Fermi gas at zero temperature. This p-wave Fermi gas is known to undergo a quantum phase transition when the inter-particle interaction is changed from the BCS to BEC regime, which is distinct from a crossover in the s-wave case. The quench dynamics of polar states of the p-wave superfluid Fermi gas is numerically studied within a mean field approach. The time evolutions of the order parameter and the momentum occupation are obtained and compared with the s-wave case. When the inter-particle interaction is quenched from BCS to BEC regime across the quantum phase transition point, the hole-burning in momentum occupation disappears in the p-wave case.
Abstract:
We develop a method for calculating nonequilibrium steady state in open quantum system that is described by a quantum master equation. We show the advantage of the method in numerical computation, and demonstrate its validity in some examples.