Finite Interaction Time Research Articles

Effekty konechnogo vremeni v odinarnom i dvoynom komptonovskom rasseyanii

The process of Compton scattering by a free electron with subsequent reemission of one or two photons is considered in the assumption of finite interaction time. The corresponding cross sections are obtained in the framework of relativistic quantum electrodynamics using a modified form of fermion propagator with complex transmitted momentum. It is shown that finite time effects can be observable at sufficiently low energies of scattered photons. The proposed method also regularizes arising infrared divergence in the cross section of the double Compton effect. Possible experimental verification of considered theoretical approach is discussed.

Finite-resolution ancilla-assisted measurements of quantum work distributions

Work is an observable quantity associated with a process; however, there is no Hermitian operator associated with its measurement. We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian via two von Neumann measurements of the system's energy carried out by a measuring apparatus modeled as a free particle of finite localization and interaction time with the system. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation. This measurement model allows us to quantify the effect that measuring has on the estimated work distribution and associated average work done on the system and average heat exchanged with the measuring apparatus.

Some Features of the Direct and Inverse Double-Compton Effect as Applied to Astrophysics

In the present paper, the process of inverse double-Compton (IDC) scattering is considered in the context of astrophysical applications. It is assumed that the two hard X-ray photons emitted from an astrophysical source are scattered on a free electron and converted into a single soft photon of optical range. Using the QED S-matrix formalism for the derivation of a cross-section of direct double-Compton (DDC) scattering and assuming detailed balance conditions, an analytical expression for the cross-section of the IDC process is presented. It is shown that at fixed energies of incident photons, the inverse cross-section has no infrared divergences, and its behavior is completely defined by the spectral characteristics of the photon source itself, in particular by the finite interaction time of radiation with an electron. Thus, even for the direct process, the problem of resolving infrared divergence actually refers to a real physical source of radiation in which photons are never actually plane waves. As a result, the physical frequency profile of the scattered radiation for DDC as well as for IDC processes is a function of both the intensity and line shape of the incident photon field.

Casimir forces and quantum friction of finite-size atoms in relativistic trajectories

We study quantum friction and Casimir forces with a full-relativistic formalism for atoms modelled as Unruh-DeWitt detectors in the presence of arbitrary macroscopic objects. We consider the general case of atoms with arbitrary relativistic trajectories in arbitrary quantum states (including coherent superpositions) close to objects that impose arbitrary boundary conditions. Particularizing for conducting plates, we show that, for relative velocities close to the speed of light, the quantum friction diverges while the Casimir force is almost independent of the velocity. Since we include the effect of the finite size of the detector and the finite interaction time, we also obtain quantum friction when the detector is isolated but follows a non-inertial trajectory.

Generation of cluster states in optomechanical quantum systems

We consider an optomechanical quantum system composed of a single cavity mode interacting with N mechanical resonators. We propose a scheme for generating continuous-variable graph states of arbitrary size and shape, including the so-called cluster states for universal quantum computation. The main feature of this scheme is that, differently from previous approaches, the graph states are hosted in the mechanical degrees of freedom rather than in the radiative ones. Specifically, via a 2N-tone laser drive, we engineer a linear Hamiltonian which is instrumental to dissipatively drive the system to the desired target state. The robustness of this scheme is assessed against finite interaction times and mechanical noise, confirming it as a valuable approach towards quantum state engineering for continuous-variable computation in a solid-state platform.

Changes in cooperative behaviour and belief in finitely repeated social dilemmas

Economic and psychological studies have determined the tendency to improve cooperation in initial interactions in which people are required to contribute in public good games. The current study examined the behavioural changes of individuals during finite interaction times. Participants were invited to make decisions twice in a step‐level public good game, and their belief in achieving the collective interest was measured. Participants were divided into three groups based on their first decisions. Results showed that high contributors demonstrated high levels of contribution in their subsequent interactions, whereas low and equal contributors increased their levels of contribution after the initial interaction. Additionally, the cooperative level of low contributors increased along with their cooperative belief. The theoretical and practical implications of changes of behaviour and belief in repeated social dilemmas were identified.

Heralded Quantum Entanglement between Distant Matter Qubits.

We propose a scheme to realize heralded quantum entanglement between two distant matter qubits using two Λ atom systems. Our proposal does not need any photon interference. We also present a general theory of outcome state of non-monochromatic incident light and finite interaction time.

Irrationality and quasiperiodicity in driven nonlinear systems.

We analyze the relationship between irrationality and quasiperiodicity in nonlinear driven systems. To that purpose, we consider a nonlinear system whose steady-state response is very sensitive to the periodic or quasiperiodic character of the input signal. In the infinite time limit, an input signal consisting of two incommensurate frequencies will be recognized by the system as quasiperiodic. We show that this is, in general, not true in the case of finite interaction times. An irrational ratio of the driving frequencies of the input signal is not sufficient for it to be recognized by the nonlinear system as quasiperiodic, resulting in observations which may differ by several orders of magnitude from the expected quasiperiodic behavior. Thus, the system response depends on the nature of the irrational ratio, as well as the observation time. We derive a condition for the input signal to be identified by the system as quasiperiodic. Such a condition also takes into account the sub-Fourier response of the nonlinear system.

Reduction of single-photon emission from a single-emitter system by intersystem crossing

We investigate the reduction in the probability of single-photon emission from a single-emitter system caused by intersystem crossing. The physical model is that a single-emitter system with three levels is excited by a square pulse laser, and then a single photon is emitted at a controllable time. We find that the intersystem crossing always reduces the probability of single-photon emission. We obtain quantitative and analytical expressions for the probabilities of zero-, one-, and two-photon emission and Mandel's Q parameter as the function of the intersystem crossing rate under the conditions of finite field strength and finite interaction time with the laser pulse. We discuss the conditions for obtaining the maximal probability of single-photon emission in the presence of intersystem crossing. We find that one can obtain a high probability of single-photon emission from the single-emitter system using square pulse excitation in comparison with continuous wave excitation. Mandel's Q parameter exhibits a transition from a sub-Poissonian behavior to a super-Poissonian behavior due to the influence of intersystem crossing. The calculated Mandel's Q parameter and second-order correlation function of photon emission considering the coherent effect are in better agreement with the experimental data.

Influence of interaction time and population redistribution on the localization of atomic excitation through electromagnetically induced transparency

We study numerically the localization of atomic excitation based on the dark states formed through electromagnetically induced transparency using interfering coupling beams. In particular, we examine the formation of dark states in a system exhibiting hyperfine splitting, including the effects of optical pumping in this multilevel system, laser polarization, and finite interaction time, and explore the conditions that lead to optimal spatial resolution of the excitation. We find that optimal localization requires long interaction times, due to the slow approach of the atomic system to steady state near the nodes of the standing wave pattern.

Laser Cooling Dynamics of Neutral Atoms in a Light Field with Nonuniform Polarization for Fixed Interaction Time

Laser cooling dynamics of neutral atoms with a closed optical transition Jg → Je in light fields with nonuniform polarization formed by counterpropagating waves with linear, circular or elliptical polarization was considered. For the case of finite interaction time of atoms with light field both mechanisms of Doppler and Sub-Doppler laser cooling affected on atoms in ensemble having different velocities were taken into account. We get qualitative relations on a base of numerical analysis in a frame of quasiclassical treatment of laser cooling. These relations allow to define optimal parameters of cooling waves, i.e. polarization, detuning from atomic resonance and intensity of light waves for the most rapid and dip laser cooling from initially wide momentum distribution for finite interaction time of atoms with laser field

Numerical calculation of dynamical friction in electron cooling systems, including magnetic field perturbations and finite time effects

The orders-of-magnitude higher luminosities required by future electron–ion collider concepts require a dissipative force to counteract the numerous factors acting to gradually increase the phase space volume of relativistic ion beams. High-energy electron cooling systems could provide the necessary dissipation via dynamical friction, but will have to be designed for new parameter regimes. It is expected that magnetic field errors, finite interaction time and other effects will reduce the dynamical friction and hence increase the cooling time, so improved understanding of the underlying dynamics is important. We present a generalized form of the classical field-free friction force equation, which conveniently captures some of these effects. Previous work (Bell et al 2008 J. Comput. Phys.227 8714) shows both numerical and conceptual subtleties associated with undersampling of strong collisions, and we present a rigorous mathematical treatment of such difficulties, based on the use of a modified Pareto distribution for the electron–ion impact parameters. We also present a very efficient numerical algorithm for calculating the dynamical friction on a single ion in the field free case. For the case of arbitrary magnetic field errors, we present numerical simulation results, showing agreement with our generalized friction force formula.

Theory of single-photon control from a two-level system source

Generation of a single photon or a pair of photons from a single emitter is important for quantum information applications. Using the generating function formalism we investigate the theory of a few photons on demand for the square laser pulse and the rapid adiabatic following method. Exact theory and numerical solutions are used to design control fields for a two level emitter, which yield an optimal single or two photon source, under the constrains of finite laser field strength and finite interaction time. Comparison to experiments of Brunel et al, shows that the experiments were made close to optimal conditions.

Theory of single photon on demand from a single molecule source

We consider the theory of single photon on demand from a two level atom or molecule source. Using optical Bloch equations and the generating function formalism we investigate three approaches to single photon control: (i) the square laser pulse; (ii) the square modulation of absorption frequency; and (iii) the rapid adiabatic following approach investigated in the experiments of Brunel et al., Phys. Rev. Lett., 1999, 83, 2722. We discuss the conditions for obtaining the maximum of the probability of emission of a single photon and a pair of photons, under the constrains of finite field strength and finite interaction time with excitation field. We obtain analytical expression for the probability of emitting zero, one, and two photons for the square pulse, and discuss semi-classical and strongly quantum limiting cases. Numerical results obtained from the generating function formalism are compared with experimental results showing that the two level system approach is suitable for the description of cryogenic temperature single molecules, and that experiments were conducted very close to the optimal conditions.

Nonadiabatic effects in atom-surface charge transfer

We present results of a joint experimental and theoretical study of the neutralization of ${\mathrm{Li}}^{+}$ ions scattered off a Ag(100) surface. Experimental data and a complete dynamical treatment based on a wave-packet propagation approach demonstrate a pronounced nonadiabatic character of the electron transfer process. In particular we show that, while strong for a fixed projectile-surface distance, the effect of the Ag(100) projected band gap on the charge transfer is to a large extent ineffective in scattering in the energy range of a few hundred eV due to the finite interaction time.

Electromagnetically induced absorption and transparency in magneto-optical resonances in an elliptically polarized field

Using a 1 to 2 transition as an analytically tractable model, we discuss in detail magneto-optical resonances of both EIA (electromagnetically induced absorption) and EIT (electromagnetically induced transparency) types in the Hanle configuration. The analysis is made for arbitrary rate of depolarizing collisions in the excited state and arbitrary elliptical field polarization. The obtained results clearly show that the main reason for the EIA sub-natural resonance is the spontaneous transfer of anisotropy from the excited level to the ground one. In the EIA case we predict the negative structures in the absortpion resonance at large field detuning. The role of the finite atom-light interaction time is briefly discussed. In addition we study non-trivial peculiarities of the resonance lineshape related to the velocity spread in a gas.

Entanglement capabilities in infinite dimensions: multidimensional entangled coherent states.

An example is given of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times. The interaction arises from a standard Kerr nonlinearity and a 50/50 beam splitter, and the initial state is a coherent state. For certain finite interaction times multidimensional generalizations of entangled coherent states are generated, for which we construct a teleportation protocol. Similarities between probabilistic teleportation and unambiguous state discrimination are pointed out.

Scaling rotationally inelastic collisions with an effective angular momentum parameter

A new formulation of the base rate and the adiabatic energy correction used in the energy corrected sudden approximation is proposed. Explicitly, the common energy gap laws are replaced with an angular momentum gap law. This law is based upon the introduction of an effective angular momentum parameter (ℓ c=2ℏ) limiting the collision-induced intra-molecular rotational energy transfer (RET) due to the finite interaction time. The experimental results of collision induced RET for the N 2–N 2, CO–CO and N 2–He systems obtained by the application of femtosecond coherent anti-Stokes Raman spectroscopy (fs-CARS) are in excellent agreement with the proposed model.

Growing-In of Optical Coherence in the FMO Antenna Complexes

We report on the novel effect of the growing-in of optical coherence in the FMO antenna complexes. The rise of coherence, monitored by femtosecond two-pulse photon echo spectroscopy at 1.27 K, occurs within a characteristic time of 150−250 fs after impulsive excitation at the red edge of the absorption spectrum and is accompanied by strong and long-lasting oscillations. We show that this effect cannot be explained in the framework of present theories for the photon echo formation. To account for the observations, we take into consideration a finite system-bath interaction time and develop the theory beyond the Markov limit. We show that the coherence does not follow the impulsive excitation promptly, instead its time development is delayed. General expressions are obtained for the nonlinear polarization, which can also be applied for analysis of other time-resolved experiments (three-pulse photon echoes, transient grating, transient absorption etc.). Model calculations fully support our experimental observations.

Coherent interaction of ion and electron beams in systems with electron cooling

A hydrodynamic approximation is used to study the behavior of dipole modes of the transverse oscillations of an ion beam in a storage ring with an electron cooling section. It is shown that in addition to the finite interaction time of the beams, instability may be caused by a specific interaction effect between the ion and electron beams in the magnetic field which leads to redistribution of energy between the various modes of the ion beam oscillations. In this case, the condition that the determinant of the transfer matrix for the cooling section does not exceed unity no longer guarantees the stability of the transverse coherent oscillations of the ion beam and all the eigenvalues of the complete matrix of the ion motion including the storage ring must be analyzed. Calculations of the stability of ion beam dipole oscillations are presented for the parameters of CELSIUS.