Two-level Subsystems Research Articles

Conditions for steady-state entanglement of quantum systems in a stationary environment under Markovian dissipation

We study the entanglement dynamics of an open quantum system composed of two identical two-level subsystems in a common stationary environment undergoing Markovian dissipation, with the help of a set of physical parameters defined with the collective transition coefficients of the system. We then systematically investigate the steady-state entanglement of such a system and obtain the necessary and sufficient condition for steady-state entanglement when it is initial-state dependent. We also show in particular conditions for steady-state entanglement in some circumstances and propose in general a conjecture for the necessary and sufficient condition when it is independent of the initial state.

Influence of coherent adiabatic excitation on femtosecond transient signals

Femtosecond laser pulses are the tools of choice for inducing and tracking the temporal evolution of electronic excitation in molecular systems. To obtain this information, a proper theoretical modeling of the observables monitored in these experiments is essential. Herein, we present a coherent approach to simulate the time-dependent signals that result from femtosecond pump-probe experiments with ionization detection. Thus, the transient signals derived from femtosecond pump-probe experiments are analyzed in terms of the coherent evolution of the energy levels perturbed by the excitation pulse. The model system is treated as the sum of independent two-level subsystems that evolve adiabatically or are permanently excited, depending on the detuning from the central wavelength of the excitation laser. This approach will allow us to explain numerically and analytically the convergence between the coherent and incoherent (rate equations) treatments for complex multi-level systems. It will be also shown that the parameter that determines the validity of the incoherent treatment is the distribution of states outside and inside the laser bandwidth, rather than the density of states as it is commonly accepted.

Laser cooling with adiabatic passage for type-II transitions

We extend the idea of laser cooling with adiabatic passage to multi-level type-II transitions. We find the cooling force can be significantly enhanced when a proper magnetic field is applied. That is because the magnetic field decomposes the multi-level system into several two-level sub-systems, hence the stimulated absorption and stimulated emission can occur in order, allowing for the multiple photon momentum transfer. We show that this scheme also works on the laser-coolable molecules with a better cooling effect compared to the conventional Doppler cooling. A reduced dependence on spontaneous emission based on our scheme is observed as well. Our results suggest this scheme is very feasible for laser cooling of polar molecules.

Counterfactual universal quantum computation

Universal quantum computation is usually associated with interaction among two-level quantum subsystems, as this interaction is commonly viewed as a necessity to achieve universal quantum computation. In this work, we show that, contrary to this intuition, universal quantum computation can be achieved without interaction among initially independent two-level quantum subsystems. We call it counterfactual universal quantum computation. As special cases, we show how to achieve counterfactual communication of quantum states, counterfactual quantum swapping, and counterfactual quantum erasure codes. To ease practical implementation, we analyze counterfactual universal quantum computation with realistic devices, including the effects of finite execution time, photon loss, and atom missing. Besides the theoretical interest of illustrating the mysterious and counterintuitive nature of quantum physics, our work has practical applications to color imaging of ancient arts, upon which light is forbidden to shine.

Optimal basis for the generalized Dicke model

A methodology is devised for building optimal bases for the generalized Dicke model based on the symmetry adapted variational solution to the problem. At order zero, the matter sector is constructed by distributing $N_a$ particles in all the possible two-level subsystems connected with electromagnetic radiation; the next order is obtained when the states of $N_a-1$ particles are added and distributed again into the two-level subsystems; and so on. In the electromagnetic sector, the order zero for each mode is the direct sum of the Fock spaces, truncated to a value of the corresponding constants of motion of each two-level subsystem; by including contributions of the other modes, the next orders are obtained. As an example of the procedure we consider $4$ atoms in the $\Xi$ configuration interacting dipolarly with two modes of electromagnetic radiation. The results may be applied to situations in quantum optics, quantum information, and quantum computing.

Assembling Large Entangled States in the Rényi-Ingarden-Urbanik Entropy Measure under the SU(2)-Dynamics Decomposition for Systems Built from Two-Level Subsystems

Assembling Large Entangled States in the Rényi-Ingarden-Urbanik Entropy Measure under the SU(2)-Dynamics Decomposition for Systems Built from Two-Level Subsystems

Quantum fluctuations of spacetime generate quantum entanglement between gravitationally polarizable subsystems

There should be quantum vacuum fluctuations of spacetime itself, if we accept that the basic quantum principles we are already familiar with apply as well to a quantum theory of gravity. In this paper, we study, in linearized quantum gravity, the quantum entanglement generation at the neighborhood of the initial time between two independent gravitationally polarizable two-level subsystems caused by fluctuating quantum vacuum gravitational fields in the framework of open quantum systems. A bath of fluctuating quantum vacuum gravitational fields serves as an environment that provides indirect interactions between the two gravitationally polarizable subsystems, which may lead to entanglement generation. We find that the entanglement generation is crucially dependent on the polarizations, i.e, they cannot get entangled in certain circumstances when the polarizations of the subsystems are different while they always can when the polarizations are the same. We also show that the presence of a boundary may render parallel aligned subsystems entangled which are otherwise unentangled in a free space. However, the presence of the boundary does not help in terms of entanglement generation if the two subsystems are vertically aligned.

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Probe readout and quantum-limited measurements

Assuming that the parameter dependent evolution, as well as the measurements that are done for readout, of a quantum system that acts as the probe in a quantum limited measurement scheme are both fixed, we find the optimal initial states of the probe that will saturate the quantum Cramer-Rao bound. When the probe system is itself made of identical, elementary, two-level subsystems or qubits, we connect the optimal state of the N qubit probe to that of the one qubit probe. This is done for two different classes of dynamics for the probe qubits, one of which is entangling while the other is not. We study the limitations placed on the optimal initial state of the probe and the achievable measurement uncertainty by restrictions on the readout procedure that is applied on the probe qubits at the end of the measurement protocol.

Virtual qubits, virtual temperatures, and the foundations of thermodynamics

We argue that thermal machines can be understood from the perspective of "virtual qubits" at "virtual temperatures": The relevant way to view the two heat baths which drive a thermal machine is as a composite system. Virtual qubits are two-level subsystems of this composite, and their virtual temperatures can take on any value, positive or negative. Thermal machines act upon an external system by placing it in thermal contact with a well-selected range of virtual qubits and temperatures. We demonstrate these claims by studying the smallest thermal machines. We show further that this perspective provides a powerful way to view thermodynamics, by analyzing a number of phenomena. This includes approaching Carnot efficiency (where we find that all machines do so essentially by becoming equivalent to the smallest thermal machines), entropy production in irreversible machines, and a way to view work in terms of negative temperature and population inversion. Moreover we introduce the idea of "genuine" thermal machines and are led to considering the concept of "strength" of work.

Energy entanglement in neutron interferometry

Entanglement between degrees of freedom, namely between the spin, path and (total) energy degrees of freedom, for single neutrons is exploited. We implemented a triply entangled Greenberger–Horne–Zeilinger(GHZ)-like state and coherently manipulated relative phases of two-level quantum subsystems. An inequality derived by Mermin was applied to analyze the generated GHZ-like state: we determined the four expectation values and finally obtained M=2.558±0.004≰2. This demonstrates the violation of a Mermin-like inequality for triply entangled GHZ-like state in a single-particle system, which, in turn, exhibits a clear inconsistency between noncontextual assumptions and quantum mechanics and confirms quantum contextuality.

Manipulation with Andreev states in spin active mesoscopic Josephson junctions

We investigate manipulation with Andreev bound states in Josephson quantum point contacts with magnetic scattering. The Rabi oscillations in the two-level Andreev subsystems are excited by resonant driving the direction of magnetic moment of the scatterer and by modulating the superconducting phase difference across the contact. The Andreev level dynamics is manifested by the temporal oscillation of the Josephson current, which is accompanied, in the case of magnetic manipulation, also by the oscillation of the Andreev states spin polarization. The interlevel transitions obey a selection rule that forbids manipulations in a certain region of external parameters and results from specific properties of Andreev bound states in magnetic contacts: $4\ensuremath{\pi}$ periodicity with respect to the superconducting phase and strong spontaneous spin polarization.

Interpreting viscosity isotherms in materials with significant structural disorder

Numerical simulations of viscosity isotherms are presented for a model system with substantial structural disorder. The system consists of an ensemble of metastable two-level subsystems, characterized individually by an elementary activation moment μ and a double well potential with a dissipation barrier Wd=μHd and a level splitting Ws=2μHs, and collectively by a distribution of equivalent fields p(Hd,Hs)=(2πσd2Hd2)−1∕2exp{−[ln(Hd∕Hdm)]2∕2σd2}×(2πσs2)−1∕2exp(−Hs2∕2σs2). The disorder is modeled with broad dispersions σd=σs∕Hdm=1.0. Under these conditions, a typical experimental observation window 10s⩽t⩽104s reveals only a short quasilogarithmic fragment of the complete relaxation isotherm. In the current investigation, we present a prescription for evaluating the thermal fluctuation field Hf=kT∕μ based on a plot of Tln(tr∕τ0) versus Ha, where tr is the “reversal time” at which an isotherm changes sign (or passes through m=0), and we discuss the merits of this approach with respect to scaling strategies.

Probing metastability with viscosity isotherms

We present a general strategy for reconstructing the temperature dependence of the thermal fluctuation field and of the spectrum of metastable state free-energy excitation barriers of any magnetic material, which exhibits persistent memory from measurements of viscosity isotherms. The prescription, which is based on the hypothesis that the free energy can be decomposed into an ensemble of two-level subsystems, is applied to the analysis of an exchange-bond-disordered ferromagnetic perovskite Ca 0.6Sr 0.4RuO 3 with a critical temperature T C∼45 K.

Investigating the Temperature Dependence of Hysteresis and Thermal Relaxation in a Ferromagnetically Ordered Perovskite

Measurements of magnetic relaxation isotherms were performed as a function of magnetic field and temperature on an exchange-bond-disordered ferromagnetic perovskite Ca <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.2</sub> Sr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.8</sub> RuO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , over an observation time window 10 slestles10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> s, and over a wide range of temperatures which spanned the entire irreversible phase. A plot of Tln(t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> /tau <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) as a function of holding field -H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> was constructed from the times t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> at which the measured relaxation isotherms reversed sign. The plot was interpreted with the aid of numerical simulations based on a model collection of two-level subsystems, which showed that the temperature dependence of the magnetic response of this perovskite was shaped by the coexistence of thermal fluctuations and the explicit evolution of the free energy landscape with temperature, and which yielded estimates for the thermal fluctuation field and for the mean intrinsic dissipation barrier as functions of temperature

A solvable model of a tracking chamber

We analyse a quantum system consisting of a particle travelling in a model-environment made up of a net of localised two-level subsystems. We examine the dynamics of the entanglement through which the environment acquires information about the direction of propagation of the particle. Our study reproduces, within a nonperturbative investigation, an old result obtained by N. F. Mott in the early days of quantum mechanics.

Pure dephasing of two charge qubits in vertically coupled quantum dots

Pure dephasing of two electrons in vertically coupled quantum dots due to the interaction with acoustic and optical phonons is calculated. We study the effect of pure dephasing on the entanglement of the two-level subsystems. Our results show the role of the size and the distance between the two quantum dots on the pure dephasing rates.

Two-Level Systems, their Evolution and Cellular Automata Method

We propose an application of the cellular automata method to a system containing many two-level subsystems similar to those governed by the Bloch vector. They are located inside one cavity and emit (or absorb) quanta of energy. We show that the system is sensitive to the probabilities of the emission and absorption of energy, and the degree of reflectivity characterising the mirrors confining the cavity. Moreover, we define and apply two entropic measures that allow monitoring the random walk of the excitations over the cavity, and changes in the chaotic character of their configuration in the system discussed.

Aging and memory effects in zero-field-cooled collections of two-level subsystems

Numerical simulations of the temperature and time dependence of the moment of a collection of thermally activated, interacting two-level subsystems, explicitly prepared under zero-field-cooled (ZFC) conditions, are presented, which clearly demonstrate that such systems do indeed exhibit aging and memory effects analogous to those observed in collectively frozen spin glasses. In particular, if zero-field cooling at a constant cooling rate is interrupted temporarily by aging in zero field at a constant temperature ${T}_{a}$ for a time $\ensuremath{\Delta}{t}_{a}$ before the system is subsequently probed by the application of a magnetic field, then the aged moment, measured either as a function of temperature $T$ on warming at a fixed rate, or as a function of observation time $\mathrm{ln}\phantom{\rule{0.2em}{0ex}}t$ at fixed temperature ${T}_{a}$, will lie below the unaged moment, and the difference between the aged and unaged response functions will exhibit an anomaly in the vicinity of either the aging temperature or the aging time, depending on the experiment which is performed.

Complete disentanglement by partial pure dephasing

We study the effect of pure dephasing on the entanglement of a pair of two-level subsystems (qubits). We show that partial dephasing induced by a super-Ohmic reservoir, corresponding to well-established properties of confined charge states and phonons in semiconductors, may lead to complete disentanglement. We show also that the disentanglement effect increases with growing distance between the two subsystems.