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We study the photon blockade at exceptional points for a non-Hermitian optomechanical system coupled to the driven whispering-gallery-mode microresonator with two nanoparticles under the weak optomechanical coupling approximation, where exceptional points emerge periodically by controlling the relative angle of the nanoparticles. We find that conventional photon blockade occurs at exceptional points for the eigenenergy resonance of the single-excitation subspace driven by a laser field, and discuss the physical origin of conventional photon blockade. Under the weak driving condition, we analyze the influences of the different parameters on conventional photon blockade. We investigate conventional photon blockade at non-exceptional points, which exists at two optimal detunings due to the eigenstates in the single-excitation subspace splitting from one (coalescence) at exceptional points to two at non-exceptional points. \textbf{Unconventional photon blockade can occur at non-exceptional points, while it does not exist at exceptional points since the destructive quantum interference cannot occur due to the two different quantum pathways to the two-photon state being not formed.} The realization of photon blockade in our proposal provides a viable and flexible way for the preparation of single-photon sources in the non-Hermitian optomechanical system., Comment: 17 pages, 13 figures

In this paper, we show how to generate the multiple single-photon wavepackets of arbitrary temporal shape from an optical cavity coupled with $N$ three-level atoms driven by a driving field in the non-Markovian regime. We derive an exact analytical expression of the optimal driving field for generating such wavepackets, which depends on two detunings of the cavity and driving field with respect to the three-level atoms. The cavity we used consists of two mirrors facing each other, where one is perfect and the other exists the dissipation (one-sided cavity), which couples with the corresponding non-Markovian input-output fields. If the first single-photon wavepacket generated by the Markovian system is the same as the non-Markovian case, the Markovian system cannot generate the same multiple single-photon wavepackets as the non-Markovian one when the spectral widths of the other environments taking values different from the spectral width of the first environment, while setting the equal spectral widths for the different environments can generate this. The generated multiple different single-photon wavepackets are not independent of each other, which satisfy certain relations with non-Markovian spectral parameters. We analyse the transition from Markovian to non-Markovian regimes and compare the differences between them, where the cavity interacts simultaneously with the multiple non-Markovian environments. Finally, we extend the above results to a general non-Markovian quantum network involving many cavities coupled with driven three-level atoms., Comment: 20 pages, 15 figures

We investigate the generation of the frequency components at the second-order sidebands based on a spinning resonator containing a degenerate optical parametric amplifier (OPA). We show an OPA driven by different pumping frequencies inside a cavity can enhance and modulate the amplitude of the second-order sideband with different influences. We find that both the second-order sideband amplitude and its associated group delay sensitively depend on the nonlinear gain of the OPA, the phase of the field driving the OPA, the rotation speed of the resonator, and the incident direction of the input fields. Tuning the pumping frequency of the OPA can remain the localization of the maximum value of the sideband efficiency and nonreciprocal behavior due to the optical Sagnac effect, which also can adjust the linewidth of the suppressive window of the second-order sideband. Furthermore, we extend the study of second-order sideband to the non-Markovian bath which consists of a collection of infinite oscillators (bosonic photonic modes). We illustrate the second-order sidebands in a spinning resonator exhibit a transition from the non-Markovian to Markovian regime by controlling environmental spectral width. \textbf{We also study the influences of the decay from the non-Markovian environment coupling to an external reservoir on the efficiency of second-order upper sidebands.} This indicates a promising new way to enhance or steer optomechanically induced transparency devices in nonlinear optical cavities and provides potential applications for precision measurement, optical communications, and quantum sensing., Comment: 24 pages, 17 figures

Shortcuts to adiabaticity are alternative fast processes which reproduce the same final state as the adiabatic process in a finite or even shorter time, which have been extended from Hermitian systems to non-Hermitian systems in recent years, but they are barely explored for general non-Hermitian systems where off-diagonal elements of the Hamiltonian are not Hermitian. In this paper, we propose a shortcuts to adiabaticity technique which is based on a transitionless quantum driving algorithm to realize population transfer for general two-level non-Hermitian systems and give both exact and approximate analytical solutions of the corresponding counteradiabatic driving Hamiltonian, where the latter can be extended to the zeroth-order and first-order terms by applying perturbative theory. We find that the first-order correction term is different from the previous results, which is caused by the non-Hermiticity of the off-diagonal elements. We work out an exact expression for the control function and present examples consisting of a general two-level system with gain and loss to show the theory. The results suggest that the high-fidelity population transfer can be implemented in general non-Hermitian systems by our method, which works even with strong non-Hermiticity and without rotating wave approximation. Furthermore, we show that the general Hamiltonian the off-diagonal elements of which are not conjugate to each other can be implemented in many physical systems with the present experimental technology, such as an atom-light interaction system and whispering-gallery microcavity, which might have potential applications in quantum information processing., Comment: 19 pages, 8 figures

We study the non-Markovian dynamics of a two-level giant atom interacting with a one-dimensional semi-infinite waveguide through multiple coupling points, where a perfect mirror is located at the endpoint of the waveguide. The system enters a non-Markovian process when the travel time of the photon between adjacent coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the giant atom. The photon released by the spontaneous emission of the atom transfers between multiple coupling points through the waveguide or is reabsorbed by the atom with the photon emitted via the atom having completed the round trip after reflection of the mirror, which leads to the photon being trapped and forming bound states. We find that three different types of bound states can be formed in the system, containing the static bound states with no inversion of population, the periodic equal amplitude oscillation with two bound states, and the periodic non-equal amplitude oscillation with three bound states. The physical origins of three bound states formation are revealed. Moreover, we consider the influences of the dissipation of unwanted modes and dephasing on the bound states. Finally, we extend the system to a more general case involving many giant atoms coupled into a one-dimensional semi-infinite waveguide. The obtained set of delay differential equations for the giant atoms might open a way to better understand the non-Markovian dynamics of many giant atoms coupled to a semi-infinite waveguide., Comment: 19 pages, 18 figures

In this work, the exact dynamics of excitation in the generalized Aubry-Andr\'{e}-Harper model coupled with an Ohmic-type environment is discussed by evaluating the survival probability and inverse participation ratio of the state of system. In contrast to the common belief that localization will preserve the information of the initial state in the system against dissipation into the environment, our study found that strong localization can enhance the dissipation of quantum information instead. By a thorough examination of the dynamics, we show that the coherent transition between the energy state of system is crucial for understanding this unusual behavior. Under this circumstance, the coupling induced energy exchange between the system and its environment can induce the periodic population of excitation on the states of system. As a result, the stable or localization-enhanced decaying of excitation can be observed, dependent on the energy difference between the states of system. This point is verified in further by checking the varying of dynamics of excitation in the system when the coupling between the system and environment is more strong., Comment: 9 pages, 5 figures

The population evolution of single excitation is studied in the Aubry- Andr\'{e}- Harper (AAH) model coupled to a $d (=1,2,3)$-dimensional simple lattices bath with a focus on the effect of localization in the system and the dimensionality of bath. By performing a precise evaluation of time-independent Schr\"{o}dinger equation, the reduced energy levels of the system can be determined. It is found that the reduce energy levels show significant relevance for the bath dimensions. Subsequently, the time evolution of excitation is studied in both the system and bath. It is found that excitation in the system can decay super-exponentially when $d=1$ or exponentially when $d=2,3$. Regarding the finite nature of bath, the spreading of excitation in the lattices bath is also studied. We find that, depending on the dimensions of bath and the initial state, the spreading of excitation in the bath is diffusive or behaves localization., Comment: 14 pages, 11 figures. Substantial revivison. Title is changed

Bound states and their influence on the dynamics of an one-dimensional tight-binding system subject to environments are studied in this paper. We identify specifically three kinds of bound states. The first is a discrete bound state (DBS), of which the energy level exhibits a gap from the continuum. The DBS exhibits the similar features of localization as the edge states in the system and thus can suppress the decay of system. The second is a bound state in the continuum (BIC), which can suppress the system decay too. It is found that the BIC is intimately connected to the edge mode of the system since both of them show almost the same features of localization and energy. The third one displays a large gap from the continuum and behaves extendible (not localized). Moreover the population of the system on this state decays partly but not all of them does. This is different from the two former bound states. The time evolution of a single excitation in the system is studied in order to illustrate the influence of the bound states. We found that both DBS and BIC play an important role in the time evolution, for example, the excitation becomes localized and not decay depending on the overlap between the initial state and the DBS or BIC. Furthermore we observe that the single excitation takes a long-range hopping when the system falls into the regime of strong localizations. This feature can be understood as the interplay of system localizations and the bath-induced long-range correlation., Comment: 15 pages

Anisotropic quantum Rabi model is a generalization of quantum Rabi model, which allows its rotating and counter-rotating terms to have two different coupling constants. It provides us with a fundamental model to understand various physical features concerning quantum optics, solid-state physics, and mesoscopic physics. In this paper, we propose an experimental feasible scheme to implement anisotropic quantum Rabi model in a circuit quantum electrodynamics system via periodic frequency modulation. An effective Hamiltonian describing the tunable anisotropic quantum Rabi model can be derived from a qubit-resonator coupling system modulated by two periodic driving fields. All effective parameters of the simulated system can be adjusted by tuning the initial phases, the frequencies and the amplitudes of the driving fields. We show that the periodic driving is able to drive a coupled system in dispersive regime to ultrastrong coupling regime, and even deep-strong coupling regime. The derived effective Hamiltonian allows us to obtain pure rotating term and counter-rotating term. Numerical simulation shows that such effective Hamiltonian is valid in ultrastrong coupling regime, and stronger coupling regime. Moreover, our scheme can be generalized to the multi-qubit case. We also give some applications of the simulated system to the Schr\"{o}dinger cat states and quantum gate generalization. The presented proposal will pave a way to further study the stronger anisotropic Rabi model whose coupling strength is far away from ultrastrong coupling and deep-strong coupling regimes in quantum optics., Comment: 5 figures

In the few-photon regime, we theoretically propose a feasible scheme to realize strong coupling optomechanical cycle in a three-mode optomechanical circulatory system (OMCS) comprising of cross-Kerr (CK) type and linear coupling between the corresponding two bosonic modes, meanwhile, where one of the bosonic modes is strongly coherently driven and the rest are weakly driven. A Langevin equation for strong three-mode OMCS is derived by adjusting the parameters of the appropriate strong coherent laser. We show that this strong coupling of optomechanical originates from the strong coherently driven the CK coupling modes, thereby, in coherent state displacement representation enhance the optomechanical coupling and present the strengthen of the nonolinearity. We obtain a set of optimal parameters by full numerical simulation of dynamics matrix, under this condition, minimal strong OMCS that exhibit a single photon perfect non-reciprocal transmission between the two optical modes, and unidirectional transportation inter the optomechanical modes. For a detection field, the system presents optomechanical induced transparency (OMIT) behavior. The presented results can be widely applied to quantum devices such as circulators, diodes, and transistors. Moreover, we brief analysis that a system which consisting of dual mechanical modes and one optical mode, further extend the system to a generalized coupled one-dimensional optomechanical array and arbitrary modes optomechanical loop network. Experimentally, the system has been demonstrated to be achieved through a variety of experimental protocols and configurations, for example optomechanical crystal and integrated quantum superconducting circuit., Comment: Further improve the use of words and grammar in the article

The spin current can result in a spin-transfer torque in the normal-metal(NM)|ferromagnetic-insulator(FMI) or normal-metal(NM)|ferromagnetic-metal(FMM) bilayer. In the earlier study on this issue, the spin relaxations were ignored or introduced phenomenologically. In this paper, considering the FMM or FMI with spin relaxations described by a non-Hermitian Hamiltonian, we derive an effective spin-transfer torque and an effective spin mixing conductance in the non-Hermitian bilayer. The dependence of the effective spin mixing conductance on the system parameters (such as insulating gap, \textit{s-d} coupling, and layer thickness) as well as the relations between the real part and the imaginary part of the effective spin mixing conductance are given and discussed. We find that the effective spin mixing conductance can be enhanced in the non-Hermitian system. This provides us with the possibility to enhance the spin mixing conductance.

Bound state and time evolution for single excitation in one dimensional XXZ spin chain within non-Markovian reservoir are studied exactly. As for bound state, a common feature is the localization of single excitation, which means the spontaneous emission of excitation into reservoir is prohibited. Exceptionally the pseudo-bound state can always be found, for which the single excitation has a finite probability emitted into reservoir. We argue that under limit $N\rightarrow \infty$ the pseudo-bound bound state characterizes an equilibrium between the localization in spin chain and spontaneous emission into reservoir. In addition, a critical energy scale for bound states is also identified, below which only one bound state exists and it also is pseudo-bound state. The effect of quasirandom disorder is also discussed. It is found in this case that the single excitation is more inclined to locate at some spin sites. Thus a many-body-localization like behavior can be found. In order to display the effect of bound state and disorder on the preservation of quantum information, the time evolution of single excitation in spin chain studied exactly by numerically solving the evolution equation. A striking observation is that the excitation can be stayed at its initial location with a probability more than 0.9 when the bound state and disorder coexist. However if any one of the two issues is absent, the information of initial state can be erased completely or becomes mixed. Our finding shows that the combination of bound state and disorder can provide an ideal mechanism for quantum memory., Comment: 12 pages, 8 figures

The technique of shortcuts to adiabaticity (STA) has attracted broad attention due to their possible applications in quantum information processing and quantum control. However, most studies published so far have been only focused on Hermitian systems under the rotating-wave approximation (RWA). In this paper, we propose a modified STA technique to realize population transfer for a non-Hermitian system without RWA. We work out an exact expression for the control function and present examples consisting of two- and three-level systems with decay to show the theory. The results suggest that the STA technique presented here is robust for fast passages. We also find that the decay has small effect on the population transfer in the three-level system. To shed more light on the physics behind this result, we reduce the quantum three-level system to an effective two-level one with large detunings. The STA technique of effective two-level system is studied. Thereby the high-fidelity population transfer can be implemented in non-Hermitian systems by our method, and it works even without RWA., Comment: 15 pages, 5 figures

In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect charge transfer processes in Photosystem II reaction center (PSII RC) inspired quantum heat engine (QHE) model in a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in details. The results show a variety of dynamical behaviours. We interpret these results in terms of noise-assisted transport effect and dynamical localization which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization dominates the dynamics and temperature modulates the balance of the two mechanisms. Furthermore, these two mechanisms can be attributed to one physical origin: bath-induced fluctuations. The two mechanisms is manifestations of dual role played by bath-induced fluctuations within respective parameter range. In addition, we find that the effec- tive voltage of QHE exhibits superior robustness with respect to the bath noise as long as the system-coupling strength is not too large.

Kubo formula gives a linear response of a quantum system to external fields, which are classical and weak with respect to the energy of the system. In this work, we take the quantum nature of the external field into account, and define a Hall conductance to characterize the linear response of a two-band system to the quantized field. The theory is then applied to topological insulators. Comparisons with the traditional Hall conductance are presented and discussed., Comment: 6 pages, 7 figures

Charge separation in light-harvesting complexes occurs in a pair of tightly coupled chlorophylls at the heart of photosynthetic reaction centers of both plants and bacteria. Recently it has been shown that quantum coherence can, in principle, enhance the efficiency of a solar cell, working like a quantum heat engine (QHE). Here, we propose a biological quantum heat engine (BQHE) motivated by Photosystem {\rm II} reaction center (PS{\rm II} RC) to describe the charge separation. Our model mainly considers two charge-separation pathways more than that in the published literature. The two pathways can interfere via cross-couplings and work together to enhance the charge-separation yields. We explore how these cross-couplings increase the current and voltage of the charge separation and discuss the advantages of multiple pathways in terms of current and power. The robustness of the BQHE against the charge recombination in natural PS{\rm II} RC and dephasing induced by environments is also explored, and extension from two pathways to multiple pathways is made. These results suggest that nature-mimicking architectures with engineered multiple pathways for charge separations might be better for artificial solar energy devices., Comment: 12 pages, 10 figures, 1 table

Understanding the mechanisms of efficient and robust energy transfer in organic systems provides us with new insights for the optimal design of artificial systems. In this paper, we explore the dynamics of excitation energy transfer (EET) through a complex quantum network by a toy model consisting of three sites coupled to environments. We study how the coherent evolution and the noise-induced decoherence work together to reach efficient EET and illustrate the role of the phase factor attached to the coupling constant in the EET. By comparing the differences between the Markovian and non-Markovian dynamics, we discuss the effect of environment and the spatial structure of system on the dynamics and the efficiency of EET. A intuitive picture is given to show how the exciton is transferred through the system. Employing the simple model, we show the robustness of EET efficiency under the influence of the environment and elucidate the important role of quantum coherence in EET. We go further to study the quantum feature of the EET dynamics by {\it quantumness} and show the importance of quantum coherence from a new respect. We calculate the energy current in the EET and its quantumness, results for different system parameters are presented and discussed., Comment: 14 pages, 7 figures

Quantum linear response theory considers only the response of a closed quantum system to a perturbation up to first order in the perturbation. This theory breaks down when the system subjects to environments and the response up to second order in perturbation is not negligible. In this paper, we develop a quantum nonlinear response theory for open systems. We first formulate this theory in terms of general susceptibility, then apply it to deriving the Hall conductance for the open system at finite temperature. Taking the two-band model as an example, we derive the Hall conductance for the two-band model. We calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model via different expressions for $d_{\alpha}(\vec p), \ \alpha=x,y,z$. The results show that the transition points of topological phase almost remain unchanged in the presence of environments., Comment: 10 pages, 6 figures

Driven two-level system is a useful model to describe many quantum objects, particularly in quantum information processing. However, the exact master equation for such a system is barely explored. Making use of the Feynman-Vernon influence functional theory, we derive an exact non-Markovian master equation for the driven two-level system and show the lost feature in the perturbative treatment for this system. The perturbative treatment leads to the time-convolutionless (TCL) and the Nakajima-Zwanzig (NZ) master equations. So to this end, we derive the time-convolutionless (TCL) and the Nakajima-Zwanzig (NZ) master equations for the system and compare the dynamics given by the three master equations. We find the validity condition for the TCL and NZ master equations. Based on the exact non-Markovian master equation, we analyze the regime of validity for the secular approximation in the time-convolutionless master equation and discuss the leading corrections of the nonsecular terms to the quantum dynamics, significant effects are found in the dynamics of the driven system., Comment: 14 pages, 9 figures. arXiv admin note: text overlap with arXiv:0907.4629 by other authors

The semiconductor diode, which acts as an electrical rectifier and allows unidirectional electronic transports, is the key to information processing in integrated circuits. Analogously, an optical rectifier (or diode) working at specific target wavelengths has recently becomes a dreaming device in optical communication and signal processing. In this paper, we propose a scheme to realize an optical diode for photonic transport at the level of few photons. The system consists of two spatially overlapping single-mode semiconductor microcavities coupled via ${\chi ^{(2)}}$ nonlinearities. The photon blockade is predicted to take place in this system. These photon blockade effects can be achieved by tuning the frequency of the input laser field (driving field). Based on those blockades, we derive analytically the single- and two-photon current in terms of zero and finite-time delayed two-order correlation function. The results suggest that the system can serve as an single- and two-photon quantum optical diodes which allow transmission of photons in one direction much more efficiently than in the other., Comment: 13 pages, 6 figures

The Hall conductivity given by the Kubo formula is a linear response of the quantum transverse transport to a weak electric field. It has been intensively studied for a quantum system without decoherence, but it is barely explored for systems subject to decoherence. In this paper, we develop a formalism to deal with this issue for topological insulators. The Hall conductance for a topological insulator coupled to an environment is derived, the derivation is based on a linear response theory of open system. As an application, the Hall conductance of a two-band topological insulator and a two-dimensional lattice is presented and discussed., Comment: 33 manuscript pages, 4 figures, http://www.nature.com/srep/2014/140924/srep06455/full/srep06455.html

Taking the non-Markovian effect into account, we study how to store a single photon of arbitrary temporal shape in a single atom coupled to an optical cavity. Our model applies to Raman transitions in three-level atoms with one branch of the transition controlled by a driving pulse, and the other coupled to the cavity. For any couplings of input field to the optical cavity and detunings of the atom from the driving pulse and cavity, we extend the input-output relation from Markovian dynamics to non-Markovian one. For most possible photon shapes, we derive an analytic expression for the driving pulse in order to completely map the input photon into the atom. We find that, the amplitude of the driving pulse depends only on the detuning of the atom from the frequency of the cavity, i.e., the detuning of the atom to the driving pulse has no effect on the strength of the driving pulse., Comment: 11 pages, 8 figures

Topological feature has become an intensively studied subject in many fields of physics. As a witness of topological phase, the edge states are topologically protected and may be helpful in quantum information processing. In this paper, we define a measure to quantify the dynamical localization of system and simulate the localization in the 1D Aubry-Andr\'{e} model. We find an interesting connection between the edge states and the dynamical localization of the system, this connection may be used as a signature of edge state and topological phase., Comment: 5 pages, 6 figures

The dynamics of atom-molecule conversion system subject to dephasing noises is studied in this paper. With the dephasing master equation and the mean-field theory, we drive a Bloch equation for the system, this equation is compared with the Bloch equation derived by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy truncation approach. Fixed points of the system are calculated by solving both the Bloch equations and the master equation, comparison between these two calculations suggests that while in a short time the mean-field theory is a good approximation for the atom-molecule conversion system, a high order hierarchy truncation approach is necessary for the system in a long time scale. Although the MFT can not predict correctly the fixed points, its prediction on the stability of the fixed points are consistent with the BBGKY theory for a wide range of parameters., Comment: 8 pages, 6 figures