Berry's phase in the two-level model

The effect of an external electric field on the quark matter is an important question due to the presence of strong electric fields in heavy ion collisions. In the lattice QCD approach, the case of a real electric field suffers from the `sign problem', and a classical electric field is often used similar as the case of chemical potential. Interestingly, in axial gauge a uniform classical electric field actually can correspond to an inhomogeneous imaginary chemical potential that varies with coordinate. On the other hand, with imaginary chemical potential, Roberge-Weiss~(R-W) phase transition occurs. In this work, the case of a uniform classical electric field is studied by using lattice QCD approach, with the emphasis on the properties of the R-W phase. Novel phenomena show up at high temperatures. It is found that, the chiral condensation oscillates with $z$ at high temperatures, and so is the absolute value of the Polyakov loop. It is verified that the charge density also oscillates with $z$ at high temperatures. The Polyakov loop can be described by an ansatz $A_p+\sum _{q=u,d} C_q\exp\left(L_τ Q_q iazeE_z\right)$, where $A_p$ is a complex number and $C_d>0,C_u\geq 0$ are real numbers that are fitted for different temperatures and electric field strengths. As a consequence, the behavior of the phase of Polyakov loop is different depending on whether the Polyakov loop encloses the origin, which implies a possible phase transition.

Vacuum pair-production in a classical electric field and an electromagnetic wave

We investigate quantum phase transitions, quantum criticality, and Berry phase for the ground state of an ensemble of non-interacting two-level atoms embedded in a non-linear optical medium, coupled to a single-mode quantized electromagnetic field. The optical medium is pumped externally through a classical electric field, so that there is a degenerate parametric amplification effect, which strongly modifies the field dynamics without affecting the atomic sector. Through a semiclassical description the different phases of this extended Dicke model are described. The quantum phase transition is characterized with the expectation values of some observables of the system as well as the Berry phase and its first derivative, where such quantities serve as order parameters. It is remarkable that the model allows the control of the quantum criticality through a suitable choice of the parameters of the non-linear optical medium, which could make possible the use of a low intensity laser to access the superradiant region experimentally.

The mathematical design of a realistic three-position quantum switch controlled by the classical electric field is suggested in form of a circular quantum well — a unit disc on a plane with four straight channels attached to it. This device implements a triple splitting of an input waveguide. The magnitude of the constant electric field directed parallel to the disc may be defined such that rotation of this field in the plane of the device permits manipulation of the electron current through the triple splitting. The problem of calculating of the current through the switch is reduced to the construction of scattered waves for the Schrödinger operator on the corresponding composite domain with the homogeneous Dirichlet conditions on the boundary. The Dirichlet boundary conditions are found to correspond most closely to real experimental conditions on the boundary of a deep quantum well. Explicit expression for transmission coefficient from one channel to another is obtained.Technically the analysis of the corresponding infinitely-dimensional spectral problem is reduced to the analysis of a relevant finite-dimensional analytic matrix function. We estimate the errors that arise from replacement of infinite-dimensional operator by the finite matrix. Our main result is the calculation of the working point of the switch in the multi-dimensional space of the numerical parameters of the switch which permits the resonance manipulation of the current.KeywordsDirichlet Boundary ConditionScattered WaveBasic DomainConstant Electric FieldHomogeneous Dirichlet Boundary ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, we study the effect of detuning parameters and driven external classical field parameters on a quantum system consisting of a ♢-configuration four-level atom inside a quantized cavity field. Under some canonical conditional of dressed states, the exact solution of the Schrödinger equation is obtained. The occupation of atomic levels and statistical population inversion is studied. Our results show that the classical field parameter dissolved the collapse periods and increased the maximum bounds of the upper state, while decreasing the lower bounds of the lower state. The detuning parameters reduce the minimum bounds of atomic levels and their inversion. On the other hand, the linear entropy and l1 norm of coherence are employed to measure the temporal evolution of the mixedness and coherence. It is found that the driven classical field improves the temporal evolution of the mixedness and lower bounds of coherence. However, the detuning parameters have a destructive effect on the mixedness and lower bounds of coherence. The intensity of the external classical field is regarded as a control parameter with different values of detuning parameters.

Theoretical study on optical response in nanostructures in the Born–Markov regime: The role of spontaneous emission and dephasing

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant.

Exact treatment of the Jaynes–Cummings model under the action of an external classical field

We introduce the general definition of the unconventional geometric phase independent of the specific physical system and show how a highly squeezed operator can approximately induce the general unconventional geometric phase, which goes beyond the original unconventional one by displacement operators (Zhu and Wang 2003 Phys. Rev. Lett. 91 187902). By means of the squeezed operator concerning the cavity mode state along a closed path in the phase space, we discuss specifically how to implement approximately a two-qubit geometric phase gate in a cavity QED system with two-photon interaction between the atoms and the cavity mode, assisted by a classical field. Discussions regarding the implementation time of the gating, the possible decaying sources and the experimental feasibility are given in detail.

We report on a numerical study of real-time dynamics of electromagnetically interacting chirally imbalanced lattice Dirac fermions within the classical statistical field theory approach. Namely, we perform exact simulations of the real-time quantum evolution of fermionic fields coupled to classical electromagnetic fields, which are in turn coupled to the vacuum expectation value of the fermionic electric current. We use Wilson-Dirac Hamiltonian for fermions, and non-compact action for the gauge field. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to transform to helicity of electromagnetic field. By performing simulations on large lattices we show that in most cases this decay process is accompanied by the inverse cascade phenomenon which transfers energy from short-wavelength to long-wavelength electromagnetic fields. In some simulations, however, we observe a very clear signature of inverse cascade for the helical magnetic fields which is not accompanied by the axial charge decay. This suggests that the relation between inverse cascade and axial charge decay is not as straightforward as predicted by the simplest form of anomalous Maxwell equations.

In classical electrodynamics, electric and magnetic fields at a point due to moving charges are calculated from the electric scalar potential and magnetic vector potential. For a moving point charge, this potential is known as Lienard–Wiechert potential and is derived in many different ways in textbooks. In this paper, we derive the retarded Lienard–Wiechert potential in a new graphical manner using space–time diagrams so that the derivation becomes more appealing and we can visualize the reason for the presence of an additional velocity-dependant factor in the denominator of the expression for the Lienard–Wiechert potential. The derivation is valid even for charged particles moving at relativistic speeds.

The influence of the external classical field on a correlated two‐mode of the electromagnetic field interacting with a three‐level atom in the Λ structure is studied. A rotation of the atomic basis is used to remove the classical field terms. The time‐dependent wave function is obtained by solving the Schrödinger equation. The influence of the classical field on the phenomenon of revival, collapse, squeezing, and marginal atomic distribution are discussed. In our analysis, the cavity field is prepared in the entangled pair coherent states and the atomic system in the upper state. The results showed that the occupation of the atomic level is significantly affected by the addition of the classical field. The presence of the classical field reduces the squeezing intervals and the extreme values of the atomic marginal distribution.

Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane

The article presents experimental results of research concerning the action of weak electric and magnetic fields on physicochemical transformations in samples of hard coal with a previously destabilized microstructure. The actions of electric and magnetic fields are fundamentally different by many parameters. It has been shown that after treatment with a weak electric field, coal posted an electret potential with an anomalously continuous charge relaxation. Compared to untreated coal samples, the rate of methane emission from methane-saturated samples is maximum for long-flame coal and decreases as it approaches anthracite. The electric field stimulates the grinding of microparticles, a decrease in the maximum gas outlet temperature, a decrease in the enthalpy value in the formation of a new phase, and an increase in the chemical activity of treated coal samples. Fundamentally different results were obtained with magnetic stimulation of coals. In X-ray diffractograms of coal powders after magnetic treatment, the values of the maxima of the main peaks are the largest in comparison with the original samples and those treated with an electric field, which is consistent with an increase in the size of microparticles in a magnetic field. There is an increase in the heat of combustion and a decrease (by 5 times) in the loss of coal mass during heating.

In this work we investigated the geometric phases of a qubit-oscillator system beyond the conventional rotating-wave approximation. We find that in the limiting of weak coupling the results coincide with that obtained under rotating-wave approximation while there exists an increasing difference with the increase of coupling constant. It was shown that the geometric phase is symmetric with respect to the sign of the detuning of the quantized field from the one-photon resonance under the conventional rotating-wave approximation while a red-blue detuning asymmetry occurs beyond the conventional rotating-wave approximation.