Classical Hamiltonian description of a two-level quantum system: The quantum Zeno effect

We consider a two-level quantum system (quantum bit), S, which can only be controlled by modulating the difference between the two energy levels. We propose a control scheme that utilizes an additional quantum bit, A, as an auxiliary system, and obtains manipulation of S through the interaction with A. For this scheme, we derive the minimum time control for any unitary transformation on the target system S, and the form of the optimal control law. We find that the optimal time protocol involves a preliminary preparation of the state of A, the control of S using interaction with A, and no simultaneous control of S and A. The optimal time is the same as the one for a controllable two level system.

Double-Fano resonance in a two-level quantum system coupled to zigzag Phosphorene nanoribbon

Using a dynamical quantum Zeno effect, we propose a general approach to control the coupling between a two-level system (TLS) and its surroundings, by modulating the energy level spacing of the TLS with a high frequency signal. We show that the TLS--surroundings interaction can be turned on or off when the ratio between the amplitude and the frequency of the modulating field is adjusted to be a zero of a Bessel function. The quantum Zeno effect of the TLS can also be observed by the vanishing of the photon reflection at these zeros. Based on these results, we propose a quantum switch to control the transport of a single photon in a 1D waveguide. Our analytical results agree well with numerical results using Floquet theory.

In this work, quantum simulation of the evolution of a two-level quantum system with a generalized anti-PT(APT)-symmetric Hamiltonian in arbitrary phase is investigated theoretically. The evolution is reinterpreted as a subsystem in a Hilbert space of higher dimensions, enabling it to construct any two-dimensional APT-symmetric Hamiltonian in a Hermitian quantum system. In some special phases, a two-qubit quantum computer is able to achieve the quantum simulation. However, a minimum six-dimensional Hilbert space is necessary for a general case, indicating that a qutrit is needed as an ancillary. We show how to realize the simulation process in a qubit-qutrit hybrid system using the duality quantum algorithm. We also give the flow chart and quantum circuit for a quantum computer of three qubits to realize the quantum simulation. Therefore, experimental realizations and applications can be expected in the future.

Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit). However, already for a three-level system (qutrit) the state space has eight dimensions, so that its complexity exceeds the grasp of our three-dimensional space of experience. This is unfortunate, given that the geometric object describing the state space of a qutrit has a much richer structure and is in many ways more representative for a general quantum system than a qubit. In this work we demonstrate that, based on the Bloch representation of quantum states, it is possible to construct a three dimensional model for the qutrit state space that captures most of the essential geometric features of the latter. Besides being of indisputable theoretical value, this opens the door to a new type of representation, thus extending our geometric intuition beyond the simplest quantum systems.

Excitation of electromagnetic waves in a waveguide with a medium, which is a two-level system, is considered. To describe the processes, both classical electrodynamics methods and quantum mechanics methods are used. The nature of the processes under study turns out to depend on the relationship between the Rabi frequency and the line width of the excited wave packet. It is shown that if the field energy density is high, then spatially inhomogeneous Rabi frequencies arise, which leads to oscillatory behavior of the wave field amplitudes. If the levels of the excited field are small, then the dynamics of the two-level quantum system becomes monotonic and the population inversion tends to zero.

The operation of a photovoltaic solar cell is discussed with a quantum two-level system as a model. A detailed-balance calculation is carried out, from which the parameters of the converter, illuminated by radiation from a black body, are exactly obtained in different geometries, taking into account radiative recombination processes. It is shown that in a 4π geometry (source fully surrounding the converter) with total radiative recombination, the thermodynamic efficiency is equal to the Carnot efficiency at zero current (open circuit): the converter behaves as an ideal thermal engine, fully reversible when delivering no power (the practical efficiency is evidently zero). The reversibility is ensured by the complete exchange of photons between the source and the converter. The current-voltage relation is obtained in all cases, and it is shown that the two-level system follows the ideal diode equation. The calculation of the thermodynamic efficiency is generalized to an energy band system (real semiconductor) with radiative recombination and is shown to be maximum at open circuit, but lower than the Carnot efficiency because of irreversibilities induced by the thermalization of carriers. The effective source temperature concept is discussed. It is shown to be valid for a two-level system, but has less physical meaning for a two-band system.

We examine the validity of the approximation in which an α particle interacting with an atom is treated classically. In order to analyse such interactions, we perform a model simulation in which the α particle is considered as a particle in one dimension, and the atom as a quantum two-level system. The particle impinges on and excites the two-level system. We treat the particle in two ways: as a quantum mechanical wave packet, and as a classical particle. The classical particle may be a point or may have an extended structure. In each case we calculate the excitation probability P21(t) as a function of time t. We focus on the situation in which the kinetic energy of the incident particle well exceeds the excitation energy of the two-level system. Although the finite-time behaviour of P21(t) varies, P21(∞) is remarkably insensitive to the size and shape of the incident wave packet in the quantum mechanical treatment. In the classical treatment, in contrast, we find that P21(∞) is sensitive to the size of the particle. The classical point particle, however, yields nearly the same values of P21(∞) as the quantum wave packet. Implications of the results on the interaction between an α particle and an atom are discussed.

In this paper we solve two equivalent time optimal control problems. On one hand, we design the control field to implement in minimum time the SWAP (or equivalent) operator on a two-level system, assuming that it interacts with an additional, uncontrollable, two-level system. On the other hand, we synthesize the SWAP operator simultaneously, in minimum time, on a pair of two-level systems subject to opposite drifts. We assume that it is possible to perform three independent control actions, and that the total control strength is bounded. These controls either affect the dynamics of the target system, under the first perspective, or, simultaneously, the dynamics of both systems, in the second view. We obtain our results by using techniques of geometric control theory on Lie groups. In particular, we apply the Pontryagin maximum principle, and provide a complete characterization of singular and nonsingular extremals. Our analysis shows that the problem can be formulated as the motion of a material point in a central force, a well known system in classical mechanics. Although we focus on obtaining the SWAP operator, many of the ideas and techniques developed in this work apply to the time optimal implementation of an arbitrary unitary operator.

We have investigated the specific issue of dynamics of co-existing phases in the Charge Ordered (CO) manganite system $Pr_0_._6_3Ca_0_._3_7MnO_3$ using the technique of conductance noise spectroscopy. We note that close to the CO transition temperature $T_c_o$ the spectral power of $Sv(f)/V^2$ deviates significantly from the 1/f frequency dependence for f \leq 0.12Hz. Our analysis shows that this deviation can be described by a single frequency Lorentzian with corner frequency $f_c$ in addition to the usual broadband 1/f noise. Such a Lorentzian contribution to $S_v(f)/V^2$ can come from a two level system (TLS). In the time serioues this shows up as RTN. For T \leq $T_c_o$ the system shows the onset of a non-linear conduction close to a threshold value $J_d_c = J_t_h$ the noise spectra is mainly 1/f in nature. $For J > J_t_h$ a large low frequency component of noise (characterized again by a frequency $f_c$) appears. We associate $f_c$ with the relaxation time tc of the TLS fluctuator so the tc = $1/f_c$. For thermal activation of the TLS the temperature dependence of $f_c$ will follow $f_c=f_oexp(-E_a/k_BT)$ where $E_a$ is an energy barrier. The value of $f_c$ shows an increase with $J_d_c$ showing that the value of the activation energy $E_a$ is being lowered by the applied bias.

The quantum Zeno effect is the inhibition of the free evolution of a system when that system is subject to a measurement process. The authors of one recent experiment study, W. M. Itano et al., [Phys. Rev. A 41, 2295 (1990)] claimed a demonstration of the quantum Zeno effect. This was done by performing discontinuous atomic-level measurements on a coherently evolving two-level atomic stystem. The measurement was implemented using a pulsed laser strong enough to saturate the two-level atomic system. In this paper, we examine the simpler case where the measurement laser is continuously on and does not saturate the two-level atomic system. In contrast to previous treatments, we show certain parameter regimes wherein an effective state reduction does occur. We ascertain the experimental parameter regimes under which a measurement can be said to have been performed. We show that, in some regimes, fully efficient photon detection does not give good information about the atomic-level populations and hence no measurement has been performed. Throughout, we emphasize that the design of an atomic level-measurement device requires more than the analysis of a mechanism for photon detection or of coherence loss. We gain insight into the operation of a particular measurement process by following the selective evolution of various systems using the quantum-trajectories approach.

We investigate a two-level quantum system driven by a Lorentzian-shaped pulse field. An analytical solution is presented in terms of the confluent Heun functions. It is shown that for specially chosen parameter conditions, there are a number of the exact analytical solutions in an explicit form. The dependence of the final transition probabilities in the two levels on the system parameters is derived analytically and confirmed numerically.

We study in detail the dynamics of unstable two-level quantum systems by adopting the Bloch-sphere formalism of qubits. By employing the Bloch-vector representation for such unstable qubit systems, we identify a novel class of critical scenarios in which the so-called energy-level and decay-width vectors, $\mathbf{E}$ and $\mathbf{\ensuremath{\Gamma}}$, are orthogonal to one another, and the parameter $r=|\mathbf{\ensuremath{\Gamma}}|/(2|\mathbf{E}|)$ is less than 1. Most remarkably, we find that critical unstable qubit systems exhibit atypical behaviors like coherence-decoherence oscillations when analyzed in an appropriately defined codecaying frame of the system. In the same frame, a unit Bloch vector $\mathbf{b}$ describing a pure critical qubit will sweep out unequal areas during equal intervals of time, while rotating about the vector $\mathbf{E}$. These phenomena emerge beyond the usual oscillatory pattern due to the energy-level difference of the two-level quantum system. Interestingly enough, we observe that these new features will persist even for quasicritical scenarios, in which the vectors $\mathbf{E}$ and $\mathbf{\ensuremath{\Gamma}}$ are not perfectly orthogonal to each other. Applications of our results to quantum information and to unstable meson-antimeson and other systems are discussed.

We discuss the appearance of Zeno or anti-Zeno effects in an exponentially decaying system. We consider the quantum dynamics of a continuously monitored two level system interacting with a squeezed bath. We find that the behavior of the system depends critically on the way in which the squeezed bath is prepared. For specific choices of the squeezing phase the system shows Zeno or anti-Zeno effects in conditions for which it would decay exponentially if no measurements were done. This result allows for a clear interpretation in terms of the equivalent spin system interacting with a fictitious magnetic field.

A general scheme of state transfer is presented for controlling the quantum system with or without an additional electromagnetic field in this paper. As an example, a two-level closed quantum system controlled by the electromagnetic field is considered. The relation between the realization of quantum logic gates and resonance magnetic field pulse is studied. Meanwhile, for a two-level open quantum system, state transfer is achieved by instantaneous projective measurements. We focus on discussing the relation between the state transfer probability and the times of measurement based on instantaneous projective measurement. The results suggest a new way to design control strategies of optimal quantum dynamics by quantum measurement.