Decoherence of quantum superpositions through coupling to engineered reservoirs

Localization effects in disordered quantum batteries

We investigate the effect of localization on the local charging of quantum batteries (QBs) modeled by disordered spin systems. Two distinct schemes based on the transverse-field random Ising model are considered, with Ising couplings defined on a Chimera graph and on a linear chain with up to next-to-nearest-neighbor interactions. By adopting a low-energy demanding charging process driven by local fields only, we obtain that the maximum extractable energy by unitary processes (ergotropy) is highly enhanced in the ergodic phase in comparison with the many-body localization (MBL) scenario. As we turn off the next-to-nearest-neighbor interactions in the Ising chain, we have the onset of the Anderson localization phase. We then show that the Anderson phase exhibits a hybrid behavior, interpolating between large and small ergotropy as the disorder strength is increased. We also consider the splitting of total ergotropy into its coherent and incoherent contributions. This incoherent part implies in a residual ergotropy that is fully robust against dephasing, which is a typical process leading to the self-discharging of the battery in a real setup. Our results are experimentally feasible in scalable systems, such as in superconducting integrated circuits.

Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka-Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.

Detection of Quantum Signals Free of Classical Noise via Quantum Correlation

Extracting useful signals is key to both classical and quantum technologies. Conventional noise filtering methods rely on different patterns of signal and noise in frequency or time domains, thus limiting their scope of application, especially in quantum sensing. Here, we propose a signal-nature-based (not signal-pattern-based) approach which singles out a quantum signal from its classical noise background by employing the intrinsic quantum nature of the system. We design a novel protocol to extract the quantum correlation signal and use it to single out the signal of a remote nuclear spin from its overwhelming classical noise backgrounds, which is impossible to be accomplished by conventional filter methods. Our Letter demonstrates the quantum or classical nature as a new degree of freedom in quantum sensing. The further generalization of this quantum nature-based method opens a new direction in quantum research.

Geometrical Bounds on Irreversibility in Squeezed Thermal Bath

Irreversible entropy production (IEP) plays an important role in quantum thermodynamic processes. Here, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a system coupled to a squeezed thermal bath subject to dissipation and dephasing, respectively. We find that the geometrical bounds of the IEP always shift in a contrary way under dissipation and dephasing, where the lower and upper bounds turning to be tighter occur in the situation of dephasing and dissipation, respectively. However, either under dissipation or under dephasing, we may reduce both the critical time of the IEP itself and the critical time of the bounds for reaching an equilibrium by harvesting the benefits of squeezing effects in which the values of the IEP, quantifying the degree of thermodynamic irreversibility, also become smaller. Therefore, due to the nonequilibrium nature of the squeezed thermal bath, the system-bath interaction energy has a prominent impact on the IEP, leading to tightness of its bounds. Our results are not contradictory with the second law of thermodynamics by involving squeezing of the bath as an available resource, which can improve the performance of quantum thermodynamic devices.

Quantum Teleportation and Dense Coding in Multiple Bosonic Reservoirs

The effect of a reservoir on quantum communication depends on its spectral density. The efficiency of quantum teleportation and dense coding is explored when each one of the channel qubits is coupled simultaneously to multiple bosonic reservoirs. It is shown that the non-Markovianity triggered by increasing the reservoir number can induce revivals of quantum advantages of the two protocols after their disappearance. However, the backflow of information to the system that signifies non-Markovianity does not always induce immediate revivals of the quantum advantages. There may be a delayed effect for some initial states, and only as the backflow of information accumulates to a certain extent can the revivals of quantum advantages be triggered.

Noisy propagation of Gaussian states in optical media with finite bandwidth

We address propagation and entanglement of Gaussian states in optical media characterised by nontrivial spectral densities. In particular, we consider environments with a finite bandwidth \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J(\omega ) = J_0 \left[ \theta (\omega -\Omega ) - \theta (\omega - \Omega - \delta )\right] $$\end{document}J(ω)=J0θ(ω-Ω)-θ(ω-Ω-δ), and show that in the low temperature regime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T\ll \Omega ^{-1}$$\end{document}T≪Ω-1: (i) secular terms in the master equation may be neglected; (ii) attenuation (damping) is strongly suppressed; (iii) the overall diffusion process may be described as a Gaussian noise channel with variance depending only on the bandwidth. We find several regimes where propagation is not much detrimental and entanglement may be protected form decoherence.

Quantum Non-Gaussianity of Multiphonon States of a Single Atom

Quantum non-Gaussian mechanical states are already required in a range of applications. The discrete building blocks of such states are the energy eigenstates-Fock states. Despite progress in their preparation, the remaining imperfections can still invisibly cause loss of the aspects critical for their applications. We derive and apply the most challenging hierarchy of quantum non-Gaussian criteria on the characterization of single trapped-ion oscillator mechanical Fock states with up to 10 phonons. We analyze the depth of these quantum non-Gaussian features under intrinsic mechanical heating and predict their requirement for reaching quantum advantage in the sensing of a mechanical force.

Work Measurement in OPEN Quantum System

Work is an important quantity in thermodynamics. In a closed quanutm system, the two-point energy measurements can be applied to measure the work but cannot be utilized in an open quantum system. With the two-point energy measurements, it has been shown that the work fluctuation satisfies the Jarzynski equality. We propose a scheme to measure the work in an open quantum system through the technique of reservoir engineering. Based on this scheme, we show that the work fluctuation in open quantum system may violate the Jarzynski equality. We apply our scheme to a two-level atom coupled to an engineered reservoir and numerically justify the general results, especially demonstrating that the second law of thermodynamics can be violated.

Protected quantum coherence by gain and loss in a noisy quantum kicked rotor

We study the effects of non-Hermiticity on quantum coherence via a noisy quantum kicked rotor (NQKR). The random noise comes from the fluctuations in kick amplitude at each time. The non-Hermitian driving indicates the imaginary kicking potential, representing the environment-induced atom gain and loss. In the absence of gain and loss, the random noise destroys quantum coherence manifesting dynamical localization, which leads to classical diffusion. Interestingly, in the presence of non-Hermitian kicking potential, the occurrence of dynamical localization is highly sensitive to the gain and loss, manifesting the restoration of quantum coherence. Using the inverse participation ratio arguments, we numerically obtain a phase diagram of the classical diffusion and dynamical localization on the parameter plane of noise amplitude and non-Hermitian driving strength. With the help of analysis on the corresponding quasieigenstates, we achieve insight into dynamical localization, and uncover that the origin of the localization is interference between multiple quasi-eigenstates of the quantum kicked rotor. We further propose an experimental scheme to realize the NQKR in a dissipative cold atomic gas, which paves the way for future experimental investigation of an NQKR and its anomalous non-Hermitian properties.

Entanglement Robustness via Spatial Deformation of Identical Particle Wave Functions

We address the problem of entanglement protection against surrounding noise by a procedure suitably exploiting spatial indistinguishability of identical subsystems. To this purpose, we take two initially separated and entangled identical qubits interacting with two independent noisy environments. Three typical models of environments are considered: amplitude damping channel, phase damping channel and depolarizing channel. After the interaction, we deform the wave functions of the two qubits to make them spatially overlap before performing spatially localized operations and classical communication (sLOCC) and eventually computing the entanglement of the resulting state. This way, we show that spatial indistinguishability of identical qubits can be utilized within the sLOCC operational framework to partially recover the quantum correlations spoiled by the environment. A general behavior emerges: the higher the spatial indistinguishability achieved via deformation, the larger the amount of recovered entanglement.

Canonical Hamiltonian ensemble representation of dephasing dynamics and the impact of thermal fluctuations on quantum-to-classical transition

An important mathematical tool for studying open quantum system theory, which studies the dynamics of a reduced system, is the completely positive and trace-preserving dynamical linear map parameterized by a special parameter-time. Counter-intuitively, akin to the Fourier transform of a signal in time-sequence to its frequency distribution, the time evolution of a reduced system can also be studied in the frequency domain. A recent proposed idea which studies the representation of dynamical processes in the frequency domain, referred to as canonical Hamiltonian ensemble representation (CHER), proved its capability of characterizing the noncalssical traits of the dynamics. Here we elaborate in detail the theoretical foundation within a unified framework and demonstrate several examples for further studies of its properties. In particular, we find that the thermal fluctuations are clearly manifested in the manner of broadening CHER, and consequently rendering the CHER less nonclassical. We also point out the discrepancy between the notions of nonclassicality and non-Markovianity, show multiple CHERs beyond pure dephasing, and, finally, to support the practical viability, propose an experimental realization based upon the free induction decay measurement of nitrogen-vacancy center in diamond.

Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion

Quantum phase transitions (QPTs) are usually associated with many-body systems in the thermodynamic limit when their ground states show abrupt changes at zero temperature with variation of a parameter in the Hamiltonian. Recently it has been realized that a QPT can also occur in a system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report an experimental demonstration of a QPT in the QRM using a ¹⁷¹Yb⁺ ion in a Paul trap. We measure the spin-up state population and the average phonon number of the ion as two order parameters and observe clear evidence of the phase transition via adiabatic tuning of the coupling between the ion and its spatial motion. An experimental probe of the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit opens up a window for controlled study of QPTs and quantum critical phenomena.

Quantum phase transition occurs in many-body systems with abrupt changes in the ground state around zero temperature. Here the authors report signatures of quantum phase transition in single trapped ion that can be described using quantum Rabi model.

Observing Information Backflow from Controllable Non-Markovian Multichannels in Diamond

The unavoidable interaction of a quantum open system with its environment leads to the dissipation of quantum coherence and correlations, making its dynamical behavior a key role in many quantum technologies. In this Letter, we demonstrate the engineering of multiple dissipative channels by controlling the adjacent nuclear spins of a nitrogen-vacancy center in diamond. With a controllable non-Markovian dynamics of this open system, we observe that the quantum Fisher information flows to and from the environment using different noisy channels. Our work contributes to the developments of both noisy quantum metrology and quantum open systems from the viewpoints of metrologically useful entanglement.

Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.

Efficient Accessible Bounds to the Classical Capacity of Quantum Channels

We present a method to detect lower bounds to the classical capacity of quantum communication channels by means of few local measurements (i.e., without complete process tomography), reconstruction of sets of conditional probabilities, and classical optimization. The method does not require any a priori information about the channel. We illustrate its performance for significant forms of noisy channels.

Quantifying the nonclassicality of pure dephasing

One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies. Dephasing processes, caused by non-dissipative information exchange between quantum systems and environments, provides a natural platform for this purpose, as they control the quantum-to-classical transition. Recently, it has been shown that dephasing dynamics itself can exhibit (non)classical traits, depending on the nature of the system-environment correlations and the related (im)possibility to simulate these dynamics with Hamiltonian ensembles–the classical strategy. Here we establish the framework of detecting and quantifying the nonclassicality for pure dephasing dynamics. The uniqueness of the canonical representation of Hamiltonian ensembles is shown, and a constructive method to determine the latter is presented. We illustrate our method for qubit, qutrit, and qubit-pair pure dephasing and describe how to implement our approach with quantum process tomography experiments. Our work is readily applicable to present-day quantum experiments.

The presence of processes that cannot be simulated classically in open quantum system dynamics is acknowledged, but an exact quantifier for this non-classical character is still missing. Here, the authors provide a quantitative measure of non-classicality for purely dephasing evolutions.

Retrieving Ideal Precision in Noisy Quantum Optical Metrology

Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) due to the photon loss in quantum metrology based on Mech-Zehnder interferometry. Here, we find that not only can the SNL be beaten, but also the ZL can be asymptotically recovered in a long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.

Dissipative Charging of a Quantum Battery

We show that a cyclic unitary process can extract work from the thermodynamic equilibrium state of an engineered quantum dissipative process. Systems in the equilibrium states of these processes serve as batteries, storing energy. The dissipative process that brings the battery to the active equilibrium state is driven by an agent that couples the battery to thermal systems. The second law of thermodynamics imposes a work cost for the process; however, no work is needed to keep the battery in that charged state. We consider simple examples of these batteries and discuss situations in which the charged state has full population inversion, in which case the extractable work is maximal, and circumstances in which the efficiency of the process is maximal.

Quantum Probes for Ohmic Environments at Thermal Equilibrium

It is often the case that the environment of a quantum system may be described as a bath of oscillators with an ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence or to tailor quantum information protocols. Recently, the use of quantum probes in characterizing ohmic environments at zero-temperature has been discussed, showing that a single qubit provides precise estimation of the cutoff frequency. On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to a complex system at thermal equilibrium. In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision attainable by quantum probes. Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e., values of the order ωc≲T (in natural units). For larger values of ωc, decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure.

Quantum self-contained refrigerator in terms of the cavity quantum electrodynamics in the weak internal-coupling regime

We present two schemes to implement the self-contained refrigerator in the framework of the cavity quantum electrodynamics. The considered refrigerators are composed of three interacting microcavities (or two microcavities simultaneously interacting with one three-level atom) separately coupling to a thermal bath with a certain temperature. Despite the local master equation employed, the proposed analytic procedure shows the perfect thermodynamical consistency. It is also demonstrated that the heat is stably extracted from the lowest temperature bath with a fixed efficiency only determined by the intrinsic properties of the refrigerators, i.e., the frequency ratio of the two cavities in contact with the two higher temperature baths. These two schemes indicate that the system with the weak internal coupling in the infinite dimensional Hilbert space can be used to realize the quantum self-contained refrigerator on the principle completely the same as the original self-contained refrigerator.

Multifunctional quantum thermal device utilizing three qubits

Quantum thermal devices which can manage heat as their electronic analogs for the electronic currents have attracted increasing attention. Here a three-terminal quantum thermal device is designed by three coupling qubits interacting with three heat baths with different temperatures. Based on the steady-state behavior solved from the dynamics of this system, it is demonstrated that such a device integrates multiple interesting thermodynamic functions. It can serve as a heat current transistor to use the weak heat current at one terminal to effectively amplify the currents through the other two terminals, to continuously modulate them ranging in a large amplitude, and even to switch on or off the heat currents. It is also found that the three currents are not sensitive to the fluctuation of the temperature at the low-temperature terminal, so it can behave as a thermal stabilizer. In addition, we can utilize one terminal temperature to ideally turn off the heat current at any one terminal and to allow the heat currents through the other two terminals, so it can be used as a thermal valve. Finally, we illustrate that this thermal device can control the heat currents to flow unidirectionally, so it has the function of a thermal rectifier.

Quantum thermal transistor based on qubit-qutrit coupling

A quantum thermal transistor is designed by the strong coupling between one qubit and one qutrit which are in contact with three heat baths with different temperatures. The thermal behavior is analyzed based on the master equation by both the numerical and the approximately analytic methods. It is shown that the thermal transistor, as a three-terminal device, allows a weak modulation heat current (at the modulation terminal) to switch on and off and effectively modulate the heat current between the other two terminals. In particular, the weak modulation heat current can induce the strong heat current between the other two terminals with the multiple-region amplification of heat current. Furthermore, the heat currents are quite robust to the temperature (current) fluctuation at the lower-temperature terminal within a certain range of temperature, and so it can behave as a heat current stabilizer.

Experimental implementation of fully controlled dephasing dynamics and synthetic spectral densities

Engineering, controlling, and simulating quantum dynamics is a strenuous task. However, these techniques are crucial to develop quantum technologies, preserve quantum properties, and engineer decoherence. Earlier results have demonstrated reservoir engineering, construction of a quantum simulator for Markovian open systems, and controlled transition from Markovian to non-Markovian regime. Dephasing is an ubiquitous mechanism to degrade the performance of quantum computers. However, all-purpose quantum simulator for generic dephasing is still missing. Here, we demonstrate full experimental control of dephasing allowing us to implement arbitrary decoherence dynamics of a qubit. As examples, we use a photon to simulate the dynamics of a qubit coupled to an Ising chain in a transverse field and also demonstrate a simulation of nonpositive dynamical map. Our platform opens the possibility to simulate dephasing of any physical system and study fundamental questions on open quantum systems.

Achieving the classical Carnot efficiency in a strongly coupled quantum heat engine

Generally, the efficiency of a heat engine strongly coupled with a heat bath is less than the classical Carnot efficiency. Through a model-independent method, we show that the classical Carnot efficiency is achieved in a strongly coupled quantum heat engine. First, we present the first law of quantum thermodynamics in strong coupling. Then, we show how to achieve the Carnot cycle and the classical Carnot efficiency at strong coupling. We find that this classical Carnot efficiency stems from the fact that the heat released in a nonequilibrium process is balanced by the absorbed heat. We also analyze the restrictions in the achievement of the Carnot cycle. The first restriction is that there must be two corresponding intervals of the controllable parameter in which the corresponding entropies of the work substance at the hot and cold temperatures are equal, and the second is that the entropy of the initial and final states in a nonequilibrium process must be equal. Through these restrictions, we obtain the positive work conditions, including the usual one in which the hot temperature should be higher than the cold, and a new one in which there must be an entropy interval at the hot temperature overlapping that at the cold. We demonstrate our result through a paradigmatic model-a two-level system in which a work substance strongly interacts with a heat bath. In this model, we find that the efficiency may abruptly decrease to zero due to the first restriction, and that the second restriction results in the control scheme becoming complex.

Synthetic clock transitions via continuous dynamical decoupling

Decoherence of quantum systems due to uncontrolled fluctuations of the environment presents fundamental obstacles in quantum science. Clock transitions which are insensitive to such fluctuations are used to improve coherence, however, they are not present in all systems or for arbitrary system parameters. Here we create a trio of synthetic clock transitions using continuous dynamical decoupling in a spin-1 Bose-Einstein condensate in which we observe a reduction of sensitivity to magnetic-field noise of up to four orders of magnitude; this work complements the parallel work by Anderson et al.. In addition, using a concatenated scheme, we demonstrate suppression of sensitivity to fluctuations in our control fields. These field-insensitive states represent an ideal foundation for the next generation of cold-atom experiments focused on fragile many-body phases relevant to quantum magnetism, artificial gauge fields, and topological matter.

Enabling the self-contained refrigerator to work beyond its limits by filtering the reservoirs

In this paper, we study the quantum self-contained refrigerator [Linden et al., Phys. Rev. Lett. 105, 130401 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.130401] in the strong internal coupling regime with engineered reservoirs. We find that if some modes of the three thermal reservoirs can be properly filtered out, the efficiency and the working domain of the refrigerator can be improved in contrast to the those in the weak internal coupling regime, which indicates one advantage of the strong internal coupling. In addition, we find that the background natural vacuum reservoir could cause the filtered refrigerator to stop working and the background natural thermal reservoir could greatly reduce the cooling efficiency.

Quantum Synchronization Blockade: Energy Quantization Hinders Synchronization of Identical Oscillators

Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization, is blocked. We demonstrate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with superconducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.

Quantum systems under frequency modulation

We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically since, with the simple two-state model providing an inexhaustible source of novel concepts. When the transition frequency of a quantum system is modulated, several phenomena can be observed, such as Landau-Zener-Stückelberg-Majorana interference, motional averaging and narrowing, and the formation of dressed states with the appearance of sidebands in the spectrum. Adiabatic changes result in the accumulation of geometric phases, which can be used to create topological states. In recent years, an exquisite experimental control in the time domain was gained through the parameters entering the Hamiltonian, and high-fidelity readout schemes allowed the state of the system to be monitored non-destructively. These developments were made in the field of quantum devices, especially in superconducting qubits, as a well as in atomic physics, in particular in ultracold gases. As a result of these advances, it became possible to demonstrate many of the fundamental effects that arise in a quantum system when its transition frequencies are modulated. The purpose of this review is to present some of these developments, from two-state atoms and harmonic oscillators to multilevel and many-particle systems.

Nonexponential Decoherence and Subdiffusion in Atom-Optics Kicked Rotor

Quantum systems lose coherence upon interaction with the environment and tend towards classical states. Quantum coherence is known to exponentially decay in time so that macroscopic quantum superpositions are generally unsustainable. In this work, slower than exponential decay of coherences is experimentally realized in an atom-optics kicked rotor system subjected to nonstationary Lévy noise in the applied kick sequence. The slower coherence decay manifests in the form of quantum subdiffusion that can be controlled through the Lévy exponent. The experimental results are in good agreement with the analytical estimates and numerical simulations for the mean energy growth and momentum profiles of an atom-optics kicked rotor.

Non-Markovian linear response theory for quantum open systems and its applications

The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.

Non-Markovianity Hierarchy of Gaussian Processes and Quantum Amplification

We investigate the dynamics of Gaussian states of continuous variable systems under Gaussianity-preserving channels. We introduce a hierarchy of such evolutions encompassing Markovian and weakly and strongly non-Markovian processes and provide simple criteria to distinguish between the classes, based on the degree of positivity of intermediate Gaussian maps. We present an intuitive classification of all one-mode Gaussian channels according to their non-Markovianity degree and show that weak non-Markovianity has an operational significance, as it leads to a temporary phase-insensitive amplification of Gaussian inputs beyond the fundamental quantum limit. Explicit examples and applications are discussed.

Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs

In this work, there are two parties, Alice on Earth and Bob on the satellite, which initially share an entangled state, and some open problems, which emerge during quantum steering that Alice remotely steers Bob, are investigated. Our analytical results indicate that all entangled pure states and maximally entangled evolution states (EESs) are steerable, and not every entangled evolution state is steerable and some steerable states are only locally correlated. Besides, quantum steering from Alice to Bob experiences a "sudden death" with increasing decoherence strength. However, shortly after that, quantum steering experiences a recovery with the increase of decoherence strength in bit flip (BF) and phase flip (PF) channels. Interestingly, while they initially share an entangled pure state, all EESs are steerable and obey Bell nonlocality in PF and phase damping channels. In BF channels, all steerable states can violate Bell-CHSH inequality, but some EESs are unable to be employed to realize steering. However, when they initially share an entangled mixed state, the outcome is different from that of the pure state. Furthermore, the steerability of entangled mixed states is weaker than that of entangled pure states. Thereby, decoherence can induce the degradation of quantum steering, and the steerability of state is associated with the interaction between quantum systems and reservoirs.

Fast Quantum Rabi Model with Trapped Ions

We show how to produce a fast quantum Rabi model with trapped ions. Its importance resides not only in the acceleration of the phenomena that may be achieved with these systems, from quantum gates to the generation of nonclassical states of the vibrational motion of the ion, but also in reducing unwanted effects such as the decay of coherences that may appear in such systems.

Ramsey Interference with Single Photons

Interferometry using discrete energy levels of nuclear, atomic, or molecular systems is the foundation for a wide range of physical phenomena and enables powerful techniques such as nuclear magnetic resonance, electron spin resonance, Ramsey-based spectroscopy, and laser or maser technology. It also plays a unique role in quantum information processing as qubits may be implemented as energy superposition states of simple quantum systems. Here, we demonstrate quantum interference involving energy states of single quanta of light. In full analogy to the energy levels of atoms or nuclear spins, we implement a Ramsey interferometer with single photons. We experimentally generate energy superposition states of a single photon and manipulate them with unitary transformations to realize arbitrary projective measurements. Our approach opens the path for frequency-encoded photonic qubits in quantum information processing and quantum communication.

Time-Resolved Observation of Thermalization in an Isolated Quantum System

We use trapped atomic ions forming a hybrid Coulomb crystal and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment. We increase the complexity of the system by adding ions and controlling coherent couplings and, thereby, we observe the emergence of thermalization: Time averages of spin observables approach microcanonical averages while related fluctuations decay. Our platform features precise control of system size, coupling strength, and isolation from the external world to explore the dynamics of equilibration and thermalization.

Spin-Orbit Interactions and Quantum Spin Dynamics in Cold Ion-Atom Collisions

We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb^{+}-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-order spin-orbit (SO) interaction as the dominant source of hyperfine relaxation in cold Yb^{+}-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb^{+} immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than is predicted by the Langevin capture theory and display a weak T^{-0.3} temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb^{+}-Li should be used to minimize hyperfine relaxation and decoherence of trapped ions in ultracold atomic gases.

A single-atom heat engine

Heat engines convert thermal energy into mechanical work and generally involve a large number of particles. We report the experimental realization of a single-atom heat engine. An ion is confined in a linear Paul trap with tapered geometry and driven thermally by coupling it alternately to hot and cold reservoirs. The output power of the engine is used to drive a harmonic oscillation. From direct measurements of the ion dynamics, we were able to determine the thermodynamic cycles for various temperature differences of the reservoirs. We then used these cycles to evaluate the power P and efficiency η of the engine, obtaining values up to P = 3.4 × 10(-22)joules per second and η = 0.28%, consistent with analytical estimations. Our results demonstrate that thermal machines can be reduced to the limit of single atoms.

Phonon arithmetic in a trapped ion system

Single-quantum level operations are important tools to manipulate a quantum state. Annihilation or creation of single particles translates a quantum state to another by adding or subtracting a particle, depending on how many are already in the given state. The operations are probabilistic and the success rate has yet been low in their experimental realization. Here we experimentally demonstrate (near) deterministic addition and subtraction of a bosonic particle, in particular a phonon of ionic motion in a harmonic potential. We realize the operations by coupling phonons to an auxiliary two-level system and applying transitionless adiabatic passage. We show handy repetition of the operations on various initial states and demonstrate by the reconstruction of the density matrices that the operations preserve coherences. We observe the transformation of a classical state to a highly non-classical one and a Gaussian state to a non-Gaussian one by applying a sequence of operations deterministically.

Cooling and Autonomous Feedback in a Bose-Hubbard Chain with Attractive Interactions

We engineer a quantum bath that enables entropy and energy exchange with a one-dimensional Bose-Hubbard lattice with attractive on-site interactions. We implement this in an array of three superconducting transmon qubits coupled to a single cavity mode; the transmons represent lattice sites and their excitation quanta embody bosonic particles. Our cooling protocol preserves the particle number-realizing a canonical ensemble-and also affords the efficient preparation of dark states which, due to symmetry, cannot be prepared via coherent drives on the cavity. Furthermore, by applying continuous microwave radiation, we also realize autonomous feedback to indefinitely stabilize particular eigenstates of the array.

Sensing Atomic Motion from the Zero Point to Room Temperature with Ultrafast Atom Interferometry

We sense the motion of a trapped atomic ion using a sequence of state-dependent ultrafast momentum kicks. We use this atom interferometer to characterize a nearly pure quantum state with n=1 phonon and accurately measure thermal states ranging from near the zero-point energy to n[over ¯]~10^{4}, with the possibility of extending at least 100 times higher in energy. The complete energy range of this method spans from the ground state to far outside of the Lamb-Dicke regime, where atomic motion is greater than the optical wavelength. Apart from thermometry, these interferometric techniques are useful for characterizing ultrafast entangling gates between multiple trapped ions.

Non-Markovian Complexity in the Quantum-to-Classical Transition

The quantum-to-classical transition is due to environment-induced decoherence, and it depicts how classical dynamics emerges from quantum systems. Previously, the quantum-to-classical transition has mainly been described with memory-less (Markovian) quantum processes. Here we study the complexity of the quantum-to-classical transition through general non-Markovian memory processes. That is, the influence of various reservoirs results in a given initial quantum state evolving into one of the following four scenarios: thermal state, thermal-like state, quantum steady state, or oscillating quantum nonstationary state. In the latter two scenarios, the system maintains partial or full quantum coherence due to the strong non-Markovian memory effect, so that in these cases, the quantum-to-classical transition never occurs. This unexpected new feature provides a new avenue for the development of future quantum technologies because the remaining quantum oscillations in steady states are decoherence-free.

Non-Markovianity of Gaussian Channels

We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.

Nontrivial quantum and quantum-like effects in biosystems: Unsolved questions and paradoxes

Non-trivial quantum effects in biological systems are analyzed. Some unresolved issues and paradoxes related to quantum effects (Levinthal's paradox, the paradox of speed, and mechanisms of evolution) are addressed. It is concluded that the existence of non-trivial quantum effects is necessary for the functioning of living systems. In particular, it is demonstrated that classical mechanics cannot explain the stable work of the cell and any over-cell structures. The need for quantum effects is generated also by combinatorial problems of evolution. Their solution requires a priori information about the states of the evolving system, but within the framework of the classical theory it is not possible to explain mechanisms of its storage consistently. We also present essentials of so called quantum-like paradigm: sufficiently complex bio-systems process information by violating the laws of classical probability and information theory. Therefore the mathematical apparatus of quantum theory may have fruitful applications to describe behavior of bio-systems: from cells to brains, ecosystems and social systems. In quantum-like information biology it is not presumed that quantum information bio-processing is resulted from quantum physical processes in living organisms. Special experiments to test the role of quantum mechanics in living systems are suggested. This requires a detailed study of living systems on the level of individual atoms and molecules. Such monitoring of living systems in vivo can allow the identification of the real potentials of interaction between biologically important molecules.

Decoherence control by quantum decoherence itself

We propose a general approach of protecting a two-level system against decoherence via quantum engineering of non-classical multiple superpositions of coherent states in a non-Markovian reservoir. The scheme surprisingly only uses the system-environment interaction responsible for the decoherence and projective measurements of the two-level system. We demonstrate the method on the example of an excitonic qubit in self-assembled semiconductor quantum dots coupled to the super-Ohmic reservoir of acoustic phonons.

Open-system dynamics of entanglement: a key issues review

One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.

Quantum harmonic oscillator state synthesis by reservoir engineering

The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems.

Detection-enhanced steady state entanglement with ions

Driven dissipative steady state entanglement schemes take advantage of coupling to the environment to robustly prepare highly entangled states. We present a scheme for two trapped ions to generate a maximally entangled steady state with fidelity above 0.99, appropriate for use in quantum protocols. Furthermore, we extend the scheme by introducing detection of our dissipation process, significantly enhancing the fidelity. Our scheme is robust to anomalous heating and requires no sympathetic cooling.