Photon-added coherent states as nonlinear coherent states

The states $|\alpha,m>$, defined as ${a^{\dagger}}^{m}|\alpha>$ up to a normalization constant and $m$ is a nonnegative integer, are shown to be the eigenstates of $f(\hat{n},m)\hat{a}$ where $f(\hat{n},m)$ is a nonlinear function of the number operator $\hat{n}$. The explicit form of $f(\hat{n},m)$ is constructed. The eigenstates of this operator for negative values of $m$ are introduced. The properties of these states are discussed and compared with those of the state $|\alpha,m >$.Comment: Rev Tex file with two figures as postscript files attached. Email: [email protected]

Multi-mode mediated exchange coupling in cavity QED

Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse exchange interaction between qubits, when they are non-resonant with the cavity but resonant with each other. We experimentally probe the inverse scaling of the inter-qubit coupling with the detuning from a cavity mode and its proportionality to the qubit-cavity interaction strength. We demonstrate that the enhanced coupling at higher frequencies is mediated by multiple higher-harmonic cavity modes. Moreover, in the case of resonant qubits, the symmetry properties of the system lead to an allowed two-photon transition to the doubly excited qubit state and the formation of a dark state.Comment: 9 pages, 6 figure

Real-time analysis of gene regulation by glucocorticoid hormones

There is increasing evidence that temporal factors are important in allowing cells to gain additional information from external factors, such as hormones and cytokines. We sought to discover how cell responses to glucocorticoids develop over time, and how the response kinetics vary according to ligand structure and concentration, and hence have developed a continuous gene transcription measurement system, based on an interleukin-6 (IL-6) luciferase reporter gene. We measured the time to maximal response, maximal response and integrated response, and have compared these results with a conventional, end point glucocorticoid bioassay. We studied natural glucocorticoids (corticosterone and cortisol), synthetic glucocorticoids (dexamethasone) and glucocorticoid precursors with weak, or absent bioactivity. We found a close correlation between half maximal effective concentration (EC50) for maximal response, and for integrated response, but with consistently higher EC50 for the latter. There was no relation between the concentration of ligand and the time to maximal response. A comparison between conventional end point assays and real-time measurement showed similar effects for dexamethasone and hydrocortisone, with a less effective inhibition of IL-6 seen with corticosterone. We profiled the activity of precursor steroids, and found pregnenolone, progesterone, 21-hydroxyprogesterone and 17-hydroxyprogesterone all to be ineffective in the real-time assay, but in contrast, progesterone and 21-hydroxyprogesterone showed an IL-6 inhibitory activity in the end point assay. Taken together, our data show how ligand concentration can alter the amplitude of glucocorticoid response, and also that a comparison between real-time and end point assays reveals an unexpected diversity of the function of glucocorticoid precursor steroids, with implications for human disorders associated with their overproduction

Reconstructing the density operator by using generalized field quadratures

The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms of the marginal distribution of these quadratures. Some examples to apply this formalism, and a reduction to the usual optical homodyne tomography are considered.Comment: 17 pages, Latex,accepted by Quantum and Semiclassical Optic

Characterizing heralded single-photon sources with imperfect measurement devices

Any characterization of a single-photon source is not complete without specifying its second-order degree of coherence, i.e., its $g^{(2)}$ function. An accurate measurement of such coherence functions commonly requires high-precision single-photon detectors, in whose absence, only time-averaged measurements are possible. It is not clear, however, how the resulting time-averaged quantities can be used to properly characterize the source. In this paper, we investigate this issue for a heralded source of single photons that relies on continuous-wave parametric down-conversion. By accounting for major shortcomings of the source and the detectors--i.e., the multiple-photon emissions of the source, the time resolution of photodetectors, and our chosen width of coincidence window--our theory enables us to infer the true source properties from imperfect measurements. Our theoretical results are corroborated by an experimental demonstration using a PPKTP crystal pumped by a blue laser, that results in a single-photon generation rate about 1.2 millions per second per milliwatt of pump power. This work takes an important step toward the standardization of such heralded single-photon sources.Comment: 18 pages, 9 figures; corrected Eq. (11) and the description follows Eq. (22

Measurement of the electric dipole moments for transitions to rubidium Rydberg states via Autler-Townes splitting

We present the direct measurements of electric-dipole moments for $5P_{3/2}\to nD_{5/2}$ transitions with $20<n<48$ for Rubidium atoms. The measurements were performed in an ultracold sample via observation of the Autler-Townes splitting in a three-level ladder scheme, commonly used for 2-photon excitation of Rydberg states. To the best of our knowledge, this is the first systematic measurement of the electric dipole moments for transitions from low excited states of rubidium to Rydberg states. Due to its simplicity and versatility, this method can be easily extended to other transitions and other atomic species with little constraints. Good agreement of the experimental results with theory proves the reliability of the measurement method.Comment: 12 pages, 6 figures; figure 6 replaced with correct versio

Extended Gaussian wave packet dynamics

We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found, and relationships are explored between the squeezed system, Gaussian wave packet dynamics, the time dependent harmonic oscillator, and wave packet dynamics in a Gauss-Hermite basis. Expressions are given for the matrix elements of the potential in some simple cases. Several examples are given, including the propagation of a non-Gaussian initial state in a Morse potential

Entangled States and Entropy Remnants of a Photon-Electron System

In the present paper an example of entanglement between two different kinds of interacting particles, photons and electrons is analysed. The initial-value problem of the Schroedinger equation is solved non-perturbatively for the system of a free electron interacting with a quantized mode of the electromagnetic radiation. Wave packets of the dressed states so obtained are constructed in order to describe the spatio-temporal separation of the subsystems before and after the interaction. The joint probability amplitudes are calculated for the detection of the electron at some space-time location and the detection of a definite number of photons. The analytical study of the time evolution of entanglement between the initially separated electron wave packet and the radiation mode leads to the conclusion that in general there are non-vanishing entropy remnants in the subsystems after the interaction. On the basis of the simple model to be presented here, the calculated values of the entropy remnants crucially depend on the character of the switching-on and off of the interaction.Comment: 12 pages, 2 figure

Hanbury Brown-Twiss interferometry and second-order correlations of inflaton quanta

The quantum theory of optical coherence is applied to the scrutiny of the statistical properties of the relic inflaton quanta. After adapting the description of the quantized scalar and tensor modes of the geometry to the analysis of intensity correlations, the normalized degrees of first-order and second-order coherence are computed in the concordance paradigm and are shown to encode faithfully the statistical properties of the initial quantum state. The strongly bunched curvature phonons are not only super-Poissonian but also super-chaotic. Testable inequalities are derived in the limit of large angular scales and can be physically interpreted in the light of the tenets of Hanbury Brown-Twiss interferometry. The quantum mechanical results are compared and contrasted with different situations including the one where intensity correlations are the result of a classical stochastic process. The survival of second-order correlations (not necessarily related to the purity of the initial quantum state) is addressed by defining a generalized ensemble where super-Poissonian statistics is an intrinsic property of the density matrix and turns out to be associated with finite volume effects which are expected to vanish in the thermodynamic limit.Comment: 42 pages, 3 included figures; corrected typos; to appear in Physical Review