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Register a new userIntegrals of motion and Robertson-Schrodinger correlated states of electromagnetic field in time-dependent linear media
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Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type Hamiltonian. Eigenstates of quadratic and linear invariants are constructed, the solutions being expressed in terms of a complex parametric function that obeys classical oscillator equation with time-varying frequency. The time evolutions of initial Glauber coherent states and Fock states are considered. The medium conductivity and the time-dependent electric permeability are shown to generate squeezing and non-vanishing covariances. In the time-evolved coherent and squeezed states all the second statistical moments of the electric and magnetic field components are calculated and shown to mminimize the Robertson-Schrodinger uncertainty relation.
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We consider the inverse problem of determining the time and space dependent electromagnetic potential of the Schrodinger equation in a bounded domain of $mathbb R^n$, $ngeq 2$, by boundary observation of the solution over the entire time span. Assuming that the divergence of the magnetic potential is fixed, we prove that the electric potential and the magnetic potential can be Holder stably retrieved from these data, whereas stability estimates for inverse time-dependent coefficients problems of evolution partial differential equations are usually of logarithmic type.
In this contribution we determine the exact solution for the ground-state wave function of a two-particle correlated model atom with harmonic interactions. From that wave function, the nonidempotent one-particle reduced density matrix is deduced. Its diagonal gives the exact probability density, the basic variable of Density-Functional Theory. The one-matrix is directly decomposed, in a point-wise manner, in terms of natural orbitals and their occupation numbers, i.e., in terms of its eigenvalues and normalized eigenfunctions. The exact informations are used to fix three, approximate, independent-particle models. Next, a time-dependent external field of finite duration is added to the exact and approximate Hamiltonians and the resulting Cauchy problem is solved. The impact of the external field is investigated by calculating the energy shift generated by that time-dependent field. It is found that the nonperturbative energy shift reflects the sign of the driving field. The exact probability density and current are used, as inputs, to investigate the capability of a formally exact independent-particle modeling in time-dependent DFT as well. The results for the observable energy shift are analyzed by using realistic estimations for the parameters of the two-particle target and the external field. A comparison with the experimental prediction on the sign-dependent energy loss of swift protons and antiprotons in a gaseous He target is made.
The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of `cat states, quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of non-classical states in cavity and circuit Quantum Electrodynamics.
We propose a method to measure the quantum state of a single mode of the electromagnetic field. The method is based on the interaction of the field with a probe qubit. The qubit polarizations along coordinate axes are functions of the interaction time and from their Fourier transform we can in general fully reconstruct pure states of the field and obtain partial information in the case of mixed states. The method is illustrated by several examples, including the superposition of Fock states, coherent states, and exotic states generated by the dynamical Casimir effect.
We solve the time-dependent Schrodinger equation describing the emission of electrons from a metal surface by an external electric field $E$, turned on at $t=0$. Starting with a wave function $psi(x,0)$, representing a generalized eigenfunction when $E=0$, we find $psi(x,t)$ and show that it approaches, as $ttoinfty$, the Fowler-Nordheim tunneling wavefunction $psi_E$. The deviation of $psi$ from $psi_E$ decays asymptotically as a power law $t^{-frac32}$. The time scales involved for typical metals and fields of several V/nm are of the order of femtoseconds.
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