Decoherence and the Loschmidt echo

Decoherence causes entropy increase that can be quantified using, e.g., the purity sigma=Trrho(2). When the Hamiltonian of a quantum system is perturbed, its sensitivity to such perturbation can be measured by the Loschmidt echo M(t). It is given by the squared overlap between the perturbed and unperturbed state. We describe the relation between the temporal behavior of sigma(t) and the average Mmacr;(t). In this way we show that the decay of the Loschmidt echo can be analyzed using tools developed in the study of decoherence. In particular, for systems with a classically chaotic Hamiltonian the decay of sigma and Mmacr; has a regime where it is dominated by the Lyapunov exponents.     

Environment-independent decoherence rate in classically chaotic systems

We study the decoherence of a one-particle system, whose classical correspondent is chaotic, when it evolves coupled to a weak quenched environment. This is done by analytical evaluation of the Loschmidt echo (i.e., the revival of a localized density excitation upon reversal of its time evolution), in the presence of the perturbation. We predict an exponential decay for the Loschmidt echo with a (decoherence) rate which is asymptotically given by the mean Lyapunov exponent of the classical system, and therefore independent of the perturbation strength, within a given range of strengths. Our results are consistent with recent experiments of polarization echoes in nuclear magnetic resonance and numerical simulations.     

Bragg scattering as a probe of atomic wave functions and quantum phase transitions in optical lattices

We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.     

Robust decoupling techniques to extend quantum coherence in diamond

We experimentally demonstrate over 2 orders of magnitude increase in the room-temperature coherence time of nitrogen-vacancy centers in diamond by implementing decoupling techniques. We show that equal pulse spacing decoupling performs just as well as nonperiodic Uhrig decoupling and also allows us to take advantage of revivals in the echo to explore the longest coherence times. At short times, we can extend the coherence of particular quantum states out from T2*=2.7 μs out to an effective T2>340 μs. For preserving arbitrary states we show the experimental importance of using pulse sequences that compensate the imperfections of individual pulses for all input states through judicious choice of the phase of the pulses. We use these compensated sequences to enhance the echo revivals and show a coherence time of over 1.6 ms in ultrapure natural abundance 13C diamond.     

Coherence freeze in an optical lattice investigated via pump-probe spectroscopy

Motivated by our observation of fast echo decay and a surprising coherence freeze, we have developed a pump-probe spectroscopy technique for vibrational states of 85Rb atoms in an optical lattice to gain information about the memory dynamics of the system. We monitor the time-dependent changes of frequencies experienced by atoms and characterize the probability distribution of these frequency trajectories. We show that the inferred distribution, unlike a naive microscopic model of the lattice, correctly predicts the main features of the observed echo decay.     

Observation of a new coherent transient in NMR — Two-pulse nutational stimulated echo in the angular distribution of gamma-radiation from oriented nuclei

A new coherent transient in NMR, the two-pulse nutational stimulated echo is reported for the ferromagnetic system⁵⁰CoFe, observed by monitoring the nuclear spin dynamics as a function of the second pulse duration via anisotropic gamma quanta from thermally oriented radioactive nuclei,⁶⁰Co. The mechanism of echo formation under strong Larmor inhomogeneous broadening and the secondary but important role of inhomogeneity associated with the rf amplitude (Rabi freqeuncy) due to skin-effect are investigated via the method of concatenation of perturbation factors in the statistical tensor formalism. For those experiments performed on time scales short compared with irreversible relaxation the theoretical predictions and subsequent experimental time-domain signals are in excellent accord. Remarkable constancy of amplitude of the new gamma-detected two-pulse echo with increase of interpulse time interval is observed, the longitudinal relaxation being manifest in the off-echo signals. Comparisons are made with NMRON four-pulse stimulated off-echo decay (analogous with conventional NMR three pulse stimulated echo) which is also sensitive to longitudinal relaxation, and with three-pulse on-echo decay (analogous with conventional NMR two-pulse Hahn echo) which measures transverse relaxation.     

Border between regular and chaotic quantum dynamics

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power-law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with [1+(q-1)(t/tau)2](1/(1-q)) (with the nonextensive entropic index q and tau depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.     

Excitable media in a chaotic flow

The response to a localized perturbation of an excitable medium under stirring by chaotic advection is investigated. It is found that below a critical stirring rate a localized perturbation produces a coherent global excitation of the system. For very slow stirring, however, the coherence of the global excitation is gradually lost. We propose a simple model to describe the effect of the flow on the excitable dynamics, and explain the observed behavior as a consequence of a steady excited filament state found in the reduced problem.     

Faster than Lyapunov decays of the classical Loschmidt echo

We show that in the classical interaction picture the echo dynamics, namely, the composition of perturbed forward and unperturbed backward Hamiltonian evolution, can be treated as a time-dependent Hamiltonian system. For strongly chaotic (Anosov) systems we derive a cascade of exponential decays for the classical Loschmidt echo, starting with the leading Lyapunov exponent, followed by a sum of the two largest exponents, etc. In the loxodromic case a decay starts with the rate given as twice the largest Lyapunov exponent. For a class of perturbations of symplectic maps the echo dynamics exhibits a drift resulting in a superexponential decay of the Loschmidt echo.     

Quantum Discord Dynamics of Three Qubits in Non-Markovian Environments

We investigate the dynamics of palrwise quantum discord （QD） for a mixed three-qubit W-type state in three independent non-Markovian reservoirs at zero temperature, each of which is modeled by a leaky cavity with Lorentzian spectral density. The influence of the environment＇s amount of non-Markovianity, the detuning between the qubit frequency and the cavity centre frequency, and the purity of the initial state on the QD dynamics are analyzed in detail. It is found that in the non-Maxkovian regime the system-reservoir interactions induce QD revivals and oscillations no matter whether the detuning is zero or not. Moreover, QD can be preserved for a long time if the non-Markovian condition and the detuning condition are satisfied simultaneously.     

Observation of an amplitude collapse and revival of chirped coherent phonons in bismuth

We have studied the A(1g) coherent phonons in bismuth generated by high fluence ultrashort laser pulses. We observed that the nonlinear regime, where the phonons' oscillation parameters depend on fluence, consists of subregimes with distinct dynamics. Just after entering the nonlinear regime, the phonons become chirped. Increasing the fluence further leads to the emergence of a collapse and revival, which next turns into multiple collapses and revivals. This is explained by the dynamics of a wave packet in an anharmonic potential, where the packet periodically breaks up and reconstitutes in its original form, giving convincing evidence that the phonons are in a quantum state, with no classical analog.     

Classically induced suppression of energy growth in a chaotic quantum system

Recent experiments with Bose–Einstein condensates (BEC) in traps and speckle potentials have explored the dynamical regime in which the evolving BEC clouds localize due to the influence of classical dynamics. The growth of their mean energy is effectively arrested. This is in contrast with the well-known localization phenomena that originate due to quantum interferences. We show that classically induced localization can also be obtained in a classically chaotic, non-interacting system. In this work, we study the classical and quantum dynamics of non-interacting particles in a double-barrier structure. This is essentially a non-KAM system and, depending on the parameters, can display chaotic dynamics inside the finite well between the barriers. However, for the same set of parameters, it can display nearly regular dynamics above the barriers. We exploit this combination of two qualitatively different classical dynamical features to obtain saturation of energy growth. In the semiclassical regime, this classical mechanism strongly influences the quantum behaviour of the system.     

Solvable model of dissipative dynamics in the deep strong coupling regime

We describe the dynamics of a qubit interacting with a bosonic mode coupled to a zero-temperature bath in the deep strong coupling (DSC) regime. We provide an analytical solution for this open system dynamics in the off-resonance case of the qubit-mode interaction. Collapses and revivals of parity chain populations and the oscillatory behavior of the mean photon number are predicted. At the same time, photon number wave packets, propagating back and forth along parity chains, become incoherently mixed. Finally, we investigate numerically the effect of detuning on the validity of the analytical solution.     

Electron spin-echo experiments in photo-excited triplet states in an external magnetic field

Electron spin-echo experiments in the photo-excited triplet states of quinoxaline-d₆ and naphthalene-d₈ at 1·2 K in an external magnetic field are presented. These include two-pulse Hahn echoes, three-pulse stimulated echoes and Carr-Purcell pulse-echo trains. The decay of the Hahn and stimulated echoes as a function of pulse interval yields measures of the spin relaxation times. Furthermore, the Hahn echo is used to obtain E.P.R. line shapes and the dynamics of the triplet sublevel populations. The angular dependence of the Hahn echo is also investigated. The Hahn echo decay time and decay modulation suggest the kind of role played by nuclear spins in the loss of electron spin phase coherence. Some promising characteristics of the pulse method are discussed.     

纳米混合分子聚集体材料中弗兰克尔激子迁移的相位弛豫

在有机染料ＰＩＣ－１中引入其衍生物ａｚａＰＩＣ－Ｉ形成能量势垒，改变在混合分子聚集体中ＰＩＣ－Ｉ的Ｊ－聚集体的实体长度。用双调制外差检测的累积光子回波技术研究了相干弗兰克尔激子失相过程。观测到激子失相时间Ｔ２随ａｚａＰＩＣ－１克分子数的增大从６０ｐｓ变为２２４ｐｓ。     

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state S, coupled to all other intra-molecular vibrational states R of the same molecule, and also to its environment Q. Molecular states forming the first reservoir R are characterized by a discrete dense spectrum, whereas the environment reservoir Q states form a continuous spectrum. Assuming the equidistant reservoir R states we find the exact analytical solution of the quantum dynamic equations. S-Q and R-Q couplings yield to spontaneous decay of the S and R states, whereas S-R exchange leads to recurrence cycles and Loschmidt echo at frequencies of S-R transitions and double resonances at the interlevel reservoir R transitions. Due to these couplings the system S time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system S dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are possible four dynamic regimes of the evolution: (i) independent of the environment Q exponential decay suppressing backward R - S transitions, (ii) Loschmidt echo regime, (iii) incoherent dynamics with multicomponent Loschmidt echo, when the system state is exchanged its energy with many states of the reservoir, (iv) cycle mixing regime, when long time system dynamics looks as a random-like. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.     

Exotic states in the dynamical Casimir effect

Inhibited decoherence has been recently observed in a dissipative two-level system by increasing the strength of the coupling with the reservoir. The system is described by the spin-boson model under a perturbation approach in the delocalized phase regime occurring in weak-coupling limit at zero temperature. Within this scenario, persistence of coherence is found over long times for various low frequency structures of the bosonic environment near a band gap. Special resonances provoke transitions in the long time dynamics if the transition amplitude of the two-level system is greater than the band gap frequency or in absence of any band gap. These transitions may hinder the the loss of coherence in the spin-boson model. Limitations of the approximations are also discussed.     

Underlying dynamics of the pedestal components in a modulated laser diode with noise

We demonstrate that the pedestal components observed in the power spectra of a directly modulated laser diode, which were interpreted as a sign of instability of the periodic regime, are an indication of the coexistence of a chaotic regime with the periodic one. We present the underlying dynamics behind the rise of these pedestals, showing two different situations in which the pedestals appear. In both, a periodic regime coexists with another attractor, a saddle cycle in one case and a chaotic attractor in the other. The random fluctuations included in the laser diode model allow the coexisting attractors to merge in the observed behavior of the laser.