Tomography vs quantum control for a three-level atom

A coherent trapping phenomenon for the level population of a three-level atom, which takes place on two-photon resonance, has been noted and well studied by a semi-classical approach where the classical electro-magnetic fields are regarded as given [1]. In this article we deal with a closed system of one or two quantized field modes and a three-level (∧-type) atom interacting to each other via the non-vanishing atomic dipole matrix elements d12 and d23 (see Fig. 1). We show that the condition for the coherent trapping determines not only the atomic state but also the field state for the two mode case. In the two mode case (see Fig. 1A), mode l (left) couples with the atom by d12 and mode r (right) by d23. The one mode case with its frequency can be regarded as a special case of the two modes with ωl = ωr = ω (see Fig. 1 B).

The dynamics of a two-level atom driven by a single laser beam and three-level atom (Lambda configuration) irradiated by two laser beams are studied taking into account of the quantized center-of-mass motion of the atom. It is shown that the trapped atom system under appropriate resonance condition exhibits the large time-scale revivals when the index of the vibrational sideband responsible for the atomic electronic transition is greater than unity. The revival times are shown to be dependent on the initial number of vibrational excitations and the magnitude of the Lamb-Dicke parameter. The sub-Poissonian statistics in vibrational quantum number is observed at certain time intervals. The minimum time of interaction for which the squeezed states of motional quadrature are generated is found to be decreasing with the increase in the Lamb-Dicke parameter.

A Superconducting QUantum Interference Device (SQUID) modulated by a fast oscillating magnetic flux can be used as a parametric amplifier, providing gain with very little added noise. Here, we develop linearized models to describe the parametrically flux-pumped SQUID in terms of an impedance. An unpumped SQUID acts as an inductance, the Josephson inductance, whereas a flux-pumped SQUID develops an additional, parallel element which we have coined the ``pumpistor.'' Parametric gain can be understood as a result of a negative resistance of the pumpistor. In the degenerate case, the gain is sensitive to the relative phase between the pump and signal. In the nondegenerate case, gain is independent of this phase. We develop our models first for degenerate parametric pumping in the three-wave and four-wave cases, where the pump frequency is either twice or equal to the signal frequency, respectively. We then derive expressions for the nondegenerate case where the pump frequency is not a multiple of the signal frequency, where it becomes necessary to consider idler tones which develop. For the nondegenerate three-wave case, we present an intuitive picture for a parametric amplifier containing a flux-pumped SQUID where current at the signal frequency depends upon the load impedance at an idler frequency. This understanding provides insight and readily testable predictions of circuits containing flux-pumped SQUIDs.

We obtain an analytical expression for the probability density of the Gaussian vector with a degenerate covariance matrix. The expression generalizes a similar expression for the nondegenerate case. A definition of the Gaussian vector on the basis of a probability density, which is common for the degenerate and nondegenerate cases, is given. Examples of using the obtained probability density for the synthesis of optimal signal-processing algorithms are presented.

In this paper we consider a geometric viewpoint to analyze the behaviour of the Conjugate Gradient (CG) method, for the solution of a symmetric linear system, when at current step a pivot breakdown possibly occurs (degenerate case). As well known this can occur when the system matrix is indefinite or singular. In the latter case the CG gets stuck, since the steplength along the current search direction cannot be computed. We show here that a simple geometric interpretation can be provided for the degenerate case, as long as some basics on projective geometry in the Euclidean space are considered.

We investigate the influence of a single-mode cavity on the Autler–Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler–Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom–cavity coupling strength g and the cavity damping κ. For an increasing g and/or decreasing κ the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double-dressing' model.

Until very recently a single atom interacting with an electromagnetic field could only be a topic of theoretical consideration because experimentally only ensembles of atoms were accessible. Atomic spectra and the probabilities of transitions in atoms had been successfully studied in atomic ensembles for a long time. Quantum mechanics enables one to calculate both spectra and probabilities. However, quantum mechanics predicts that any transition happens at a random moment of time. In accordance with this prediction a single atom irradiated by light will make random jumps between its ground and excited electronic states. However, these jumps cannot be observed if we detect emission from the whole atomic ensemble, because a statistical average hides the random character of the processes. Therefore they cannot be observed in ensembles. This is only one example of new aspects which emerge when we move from atomic ensembles to a single atom. In this book we intend to discuss not only problems of probabilistic and spectral calculations, but also various random characteristics of atoms and molecules, the so-called quantum trajectories, which are typical in the spectroscopy of single atoms or molecules. In order to prepare for the discussion of quantum trajectories, we have to discuss the basic principles underlying the spectroscopy of a single two-level atom interacting with a transverse electromagnetic field.

The interaction of a three-level atom with the electromagnetic field of a quantum cavity in the presence of a laser field presents a rich behavior in the dispersive regime that we exploit to discuss two quantum batteries. In the first setup, we consider a single three-level atom interacting sequentially with many cavities, each in a thermal state. We show that under this process, the atom converges towards an equilibrium state that displays population inversion. In the second setup, a stream of atoms in a thermal state interacts sequentially with a single cavity initially in a thermal state at the same temperature as the atoms. We show that the cavity’s energy increases continuously as the stream of atoms continues to cross, and the cavity does not reach an equilibrium state. After many atoms have traveled, the cavity’s state becomes active, storing extractable energy that increases in proportion to the work done by the laser. However, the same dynamics may involve only two cavity levels in an interesting limit called the highly selective regime. In that regime, the cavity reaches an equilibrium state similar to the one of the atom in the first scenario. The charging process we propose is robust. We discuss its thermodynamics and evaluate the energy supplied by the laser, the energy stored in the battery, and, thus, the device’s efficiency. We also analyze the role of damping.

A coherent dynamics of two-and three-level atoms in the ideal cavity were investigated. In particular, the investigation of the dynamics of three-level atoms (qutrits) interacting with photons in the cavity having two resonant frequencies close to the frequencies of the two allowed atomic transitions were performed. This model generalizes the well-known Tavis-Cummings model. Time dependencies of mean number of the cavity photons and level populations of atoms are computed and entanglement of atoms and photon fields states are discussed.

We experimentally demonstrate cavity field control by another laser beam with three-level \ensuremath{\Lambda}-type atoms inside an optical ring cavity. By adjusting the frequency detuning of the controlling beam (coupled to one of the atomic transitions), the intensity of the cavity field interacting with another atomic transition is switched on and off. Such all-optical switching between two steady states is caused by the enhanced Kerr nonlinearity due to atomic coherence in such system.

Interference spectra induced by a bichromatic field in the excited state of a three-level atom

Alternative scheme to generate a supersinglet state of three-level atoms

Is an atom more likely to scatter a photon with an exponentially rising or decaying temporal profile? We try to answer this question experimentally and investigate the scattering of heralded photons from a single atom in free-space [1]. We use a single Rubidium atom trapped in optical tweezers and prepared in the groundstate of a cyclic dipole transition as a textbook-like two-level system. A time-ordered photon pair source, in conjunction with an asymmetric cavity, generates heralded single photons with an exponentially decaying or rising temporal profile [2, 3]. The heralded photons are resonant with the atomic transition and have a bandwidth comparable to the atomic linewidth. The photons are strongly focused onto the atom by a large numerical aperture lens. We study the scattering dynamics by measuring the atomic emission and the reduction in the number of transmitted photons. We perform the scattering experiment for photons with exponentially decaying and rising temporal envelopes and find that the atomic dynamics depend on the temporal profile of the photon. The atomic absorption is shorter but has a higher maximum for the rising photon than for the the decaying one. Interestingly, the overall probability that the photon is scattered by the atom is similar for decaying and rising photons.

This paper deals with multichannel time series, and extends the autocorrelation method for fitting the time series from the nondegenerate case to the general case. We shall show that the AR model obtained by solving the normal equations is always stable even in the degenerate case. The multichannel Levinson algorithm for solving the normal equations is extended from the nondegenerate case to the general case. In the nondegenerate case, the first n+1 values of the auto-correlation sequence of the obtained AR model of order n are identical with those of the original data. The next considered is the extrapolation problem of an autocorrelation sequence, that is, given data <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{R_{0}, R_{1},..., R_{n}}</tex> , it is to construct a model whose first n+1 values of the autocorrelation sequence are identical with these data. We shall show that, even in the degenerate case, when the given data <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{R_{0}, R_{1},..., R_{n}}</tex> are taken from the autocorrelation sequence of a purely nondeterministic time series, they are identical with the first n+1 values of the autocorrelation sequence of the AR model of order n.

Carbon-bridged atomically dispersed platinum on MOF-derived ZnO/C for selective photocatalytic oxidation of NO into Nitrates and Nitrites