Wei-Min Zhang

It is known that the opening or closing mechanism of a voltage-gated ion channel is triggered by the potential difference across the cell membrane in the nervous system. Based on this picture, we model the ion channel as a nanoscale two-terminal ionic tunneling junction. We apply an external time-varying voltage on the junction to mimic the membrane potential difference in the stimulation of neurons. We derive the non-Markovian quantum Langevin equation from the first principle of quantum mechanics for the ion transport in ion channels, and obtain the ion transport current in terms of quantum tunnelings of ions controlled by the time-varying voltage. We find that the time-varying voltage induces an effective magnetic flux, which causes quantum coherence in ion tunnelings. This effective magnetic flux induces further an oscillatory component to the spectral structure of the ion system, forming a time-dependent quantum memory. Such voltage-induced memory is defined as the active quantum memory, which manifests in the system with a regular oscillatory sideband structure in the ion transport current. The sideband structure demonstrates a multicrossing hysteresis in the current-voltage ( I − V ) curve, responding to the variation of the time-varying voltage (membrane potential difference). We also find that the strength of active quantum memory can be described by the ratio of amplitude and frequency of the time-varying voltage, and can be quantitatively measured through the number of nonzero cross points in the I − V hysteresis and conductance-voltage diagram. Additionally, we explore the temperature dependence of the active quantum memory in such a system. Further, we apply this model to the ion channel system on the biological energy scale. The description of these active quantum memory characteristics provides a quantum mechanical understanding to the underlying mechanism of ion channel dynamics.

Utilizing the general theory of open quantum systems to investigate the exact dynamical evolution of simple bilinear systems, we discover a mechanism of the dynamical genesis of quantum entanglement. We focus in detail on the exact quantum evolution dynamics of two photonic modes (or any two bosonic modes) coupled to each other through a linear interaction, as the simplest system of open quantum systems that we have investigated in the past two decades. Such a linear coupling alone fails to produce two-mode entanglement. We also start with an initially separable pure state of the two modes. By solving exactly the quantum equation of motion without relying on the probabilistic interpretation, we find that when the initial state of one mode is different from a coherent state (a minimum uncertainty wave packet with equal variance in the conjugate quadratures that corresponds to a well-defined classically “particle”), the causality in the time-evolution of each mode is internally violated. It also leads to the emergence of quantum entanglement between the two modes. The lack of causality is the nature of statistics. We discover that it is the internal violation of causality in the reduced (subsystem) dynamical evolution that results in the emergence of entanglement and statistic probability in quantum mechanics, even though the dynamical evolution of the whole system completely obeys the deterministic Schrödinger equation. This conclusion is valid for the quantum dynamics of more complicated composite systems. It may provide the fundamental mechanism of the dynamical genesis for both the entanglement and the statistical probability within the deterministic framework of quantum mechanics, which is the longest-standing problem that has not been fully understood since the birth of quantum mechanics.

The opening or closing mechanism of a voltage-gated ion channel is triggered by the potential difference crossing the cell membrane in the nervous system. Based on this picture, we model the ion channel as a nanoscale two-terminal ionic tunneling junction. External time-varying voltage exerting on the two-terminal ionic tunneling junction mimics the stimulation of neurons from the outside. By deriving the quantum Langevin equation from quantum mechanics, the ion channel current is obtained by the quantum tunneling of ions controlled by the time-varying voltage. The time-varying voltage induces an effective magnetic flux which causes quantum coherence in ion tunnelings and leads to sideband effects in the ion channel current dynamics. The sideband effects in the ionic current dynamics manifest a multi-crossing hysteresis in the I-V curve, which is the memory dynamics responding to the variation of the external voltage. Such memory dynamics is defined as the active quantum memory with respect to the time-varying stimuli. We can quantitatively describe how active quantum memory is generated and changed. We find that the number of the non-zero cross points in the I-V curve hysteresis and the oscillation of the differential conductance are the characteristics for quantitatively describing the active quantum memory. We also explore the temperature dependence of the active quantum memory in such a system. The discovery of this active quantum memory characteristics provides a new understanding about the underlying mechanism of ion channel dynamics.

Dissipationless localized bound states of open quantum systems are significantly robust to decoherence and have potential applications in quantum technologies. In this work, the decoherence dynamics and dissipationless localized bound states of a two-mode open quantum system are investigated. The conditions for the emergence of dissipationless localized bound states are analytically solved, and the corresponding critical system-environment couplings under different values of the inter-mode coupling and the detuning are determined. The decoherence dynamics of the system under such conditions are analyzed and dissipationless coherence between the different localized bound states against decoherence is clearly shown. This may provide a new avenue to develop dissipationless quantum technology for quantum operations.

We derive the quantum thermodynamics of quantum Brownian motion from the exact solution of its reduced density matrix. We start from the total equilibrium thermal state between the Brownian particle and its reservoir, and solve analytically and exactly the reduced density matrix of the system by taking the partial trace over all the reservoir states. We find that the reduced Hamiltonian and the reduced partition function of the Brownian motion must be renormalized significantly, as shown in the general nonperturbative renormalization theory of quantum thermodynamics for open quantum systems we developed recently [ Phys. Rev. Res. 4, 023141 (2022)]. The reduced Hamiltonian contains not only a frequency shift but also a squeezing pairing interaction, where a momentum-dependent potential is generated naturally from the strong coupling between the Brownian particle and the reservoir, after traced over all the reservoir states. The resulting exact reduced density matrix of the Brownian motion is given by a squeezing thermal state. Moreover, beyond the weak-coupling limit, in order to obtain correctly the reduced partition function of the Brownian motion, one must take into account the non-negligible changes of the reservoir state induced by the system-reservoir coupling. Using the exact solutions of the reduced density matrix, the reduced Hamiltonian, as well as the reduced partition function of the Brownian motion, we show that the controversial results obtained from the different definitions of internal energy and the issue of the negative heat capacity in the previous studies of strong-coupling quantum thermodynamics are resolved.

We present a quantum transport theory for hybrid superconducting systems based on our exact master equation approach. The total transient transport current is decomposed into components that describe coherent transports through different paths of particle and hole channels. We show that the coherent transports are resultant interferences of numerous repeated tunneling processes and cannot be rendered as a simple normal transmission or Andreev reflection as usually described quantum transport involving superconductivity. As a practical application, we find that the coherent transport currents passing through a pair of well-separated Majorana zero modes vanish due to the totally destructive interference between the particle and hole channels.

We present a quantum transport theory for hybrid superconducting systems based on our exact master-equation approach. The system-terminal transport current dynamics are fully captured by the extended nonequilibrium Green's function incorporating pair correlations via spectral density matrices. The total transient transport current is decomposed into components that describe coherent transports through different paths of particle and hole channels. We show that these coherent transports are resultant interferences of numerous repeated tunneling processes and cannot be rendered as a simple normal transmission or Andreev reflection as usually described in the steady quantum transport involving superconductivity. As a practical application, we apply the theory to a two-terminal superconductor-semiconductor nanowire to study the transport dynamics through a pair of Majorana zero modes. We find that the coherent transport currents passing through a pair of well-separated Majorana zero modes vanish due to the totally destructive interference between the particle and hole channels. This provides a different understanding to the scenario of “teleportation” via a pair of delocalized Majorana zero modes, namely, a pair of delocalized Majorana zero modes does not possess the nonlocality of an entangled pair for quantum teleportation.

In this paper, we investigate the strong-coupling quantum thermodynamics of a hybrid quantum system far from equilibrium, based on the renormalization theory of quantum thermodynamics we developed recently [ Phys. Rev. Research 4, 023141 (2022)]. The strong-coupling hybrid system consists of a superconducting microwave cavity and a spin ensemble of the NV centers in diamond under external driving. The non-Markovian dynamics of this strong-coupling hybrid system has been experimentally explored and theoretically investigated. We apply the renormalization theory of quantum thermodynamics to study the transient quantum heat and work in this strong-coupling hybrid system. We find that the dissipation and fluctuation dynamics of the system induce the transient quantum heat current which shows significant non-Markovian effects. On the other hand, the energy and driving field renormalization produces quantum work power. In particular, the driving-induced work power can be largely enhanced by non-Markovian dynamics through the cavity coupling strongly with the spin ensemble at the resonance. Our results show that non-Markovian dynamics makes faster energy conversion of the heat and work.