Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator

Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\epsilon = -\partial_x^2 + x^2 + i\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued function and $\epsilon > 0$ a small parameter. We define $\Sigma(\epsilon)$ as the infimum of the real part of the spectrum of $H_\epsilon$, and $\Psi(\epsilon)^{-1}$ as the supremum of the norm of the resolvent of $H_\epsilon$ along the imaginary axis. Under appropriate conditions on $f$, we show that both quantities $\Sigma(\epsilon)$, $\Psi(\epsilon)$ go to infinity as $\epsilon \to 0$, and we give precise estimates of the growth rate of $\Psi(\epsilon)$. We also provide an example where $\Sigma(\epsilon)$ is much larger than $\Psi(\epsilon)$ if $\epsilon$ is small. Our main results are established using variational "hypocoercive" methods, localization techniques and semiclassical subelliptic estimates.Comment: 38 pages, 4 figure

Creating collective many-body states with highly excited atoms

We study the collective excitation of a gas of highly excited atoms confined to a large spacing ring lattice, where the ground and the excited states are coupled resonantly via a laser field. Our attention is focused on the regime where the interaction between the highly excited atoms is very weak in comparison to the Rabi frequency of the laser. We demonstrate that in this case the many-body excitations of the system can be expressed in terms of free spinless fermions. The complex many-particle states arising in this regime are characterized and their properties, e.g. their correlation functions, are studied. In addition we investigate how one can actually experimentally access some of these many-particle states by a temporal variation of the laser parameters.Comment: 10 pages, 7 figure

Photoionization Rates of Cs Rydberg Atoms in a 1064 nm Far Off-Resonance Trap

Experimental measurements of photoionization rates of $nD_{5/2}$ Rydberg states of Cs ($50 \leq n \leq 75$) in a 1064 nm far off-resonance dipole trap are presented. The photoionization rates are obtained by measuring the lifetimes of Rydberg atoms produced inside of a 1064 nm far off-resonance trap and comparing the lifetimes to corresponding control experiments in a magneto-optical trap. Experimental results for the control experiments agree with recent theoretical predictions for Rydberg state lifetimes and measured photoionization rates are in agreement with transition rates calculated from a model potential.Comment: 12 pages, 4 figure

Quasiclassical calculations of BBR-induced depopulation rates and effective lifetimes of Rydberg nS, nP and nD alkali-metal atoms with n < 80

Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal \textit{nS}, \textit{n}P and \textit{nD} Rydberg states have been calculated in a wide range of principal quantum numbers $n \le 80$ at the ambient temperatures of 77, 300 and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.Comment: 12 pages, 6 figures, 8 tables. Typo in Eq.16 corrected in V2. Typos in Eq.5 and Eq.9 corrected in V3. Error in calculation of Rb nP_{3/2} effective lifetimes corrected in V4: see new data in Table II and Table VII, Erratum to be published in PR

Effect of finite detection efficiency on the observation of the dipole-dipole interaction of a few Rydberg atoms

We have developed a simple analytical model describing multi-atom signals that are measured in experiments on dipole-dipole interaction at resonant collisions of a few Rydberg atoms. It has been shown that finite efficiency of the selective field-ionization detector leads to the mixing up of the spectra of resonant collisions registered for various numbers of Rydberg atoms. The formulas which help to estimate an appropriate mean Rydberg atom number for a given detection efficiency are presented. We have found that a measurement of the relation between the amplitudes of collisional resonances observed in the one- and two-atom signals provides a straightforward determination of the absolute detection efficiency and mean Rydberg atom number. We also performed a testing experiment on resonant collisions in a small excitation volume of a sodium atomic beam. The resonances observed for 1 to 4 detected Rydberg atoms have been analyzed and compared with theory.Comment: 10 pages, 4 figures; equations 8,9,18,19,23,26-31, figures 3 and 4(d), and measurements revised in version

Ionization of Sodium and Rubidium nS, nP and nD Rydberg atoms by blackbody radiation

Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nS, nP and nD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependencies on n. The calculated ionization rates are compared with the results of our earlier measurements of BBR-induced ionization rates of Na nS and nD Rydberg states with n=8-20 at 300 K. A good agreement for all states except nS with n>15 is observed. We also present the useful analytical formulae for quick estimation of BBR ionization rates of Rydberg atoms.Comment: 14 pages, 6 figures, 6 tables in Appendi

A comparison of star formation characteristics in different types of irregular galaxies

Two regions of recent star formation in blue irregular galaxies were observed with the IUE in the short wavelength, low dispersion mode. The spectra indicates that the massive star content is similar in these regions and is best fit by massive stars formed in a burst and now are approximately 2.5 to 3.0 million years old

Strongly correlated gases of Rydberg-dressed atoms: quantum and classical dynamics

We discuss techniques to generate long-range interactions in a gas of groundstate alkali atoms, by weakly admixing excited Rydberg states with laser light. This provides a tool to engineer strongly correlated phases with reduced decoherence from inelastic collisions and spontaneous emission. As an illustration, we discuss the quantum phases of dressed atoms with dipole-dipole interactions confined in a harmonic potential, as relevant to experiments. We show that residual spontaneous emission from the Rydberg state acts as a heating mechanism, leading to a quantum-classical crossover.Comment: 4 pages, 4 figure

Spectral properties of a Rydberg atom immersed in a Bose-Einstein condensate

The electronic spectrum of a Rydberg atom immersed in a Bose-Einstein condensate is investigated. The Heisenberg equations of motions for the condensate and the Rydberg atom are derived. Neglecting the backaction of the Rydberg atom onto the condensate decouples the equations describing the condensate and Rydberg atom. In this case the spectral structure of the Rydberg atom is completely determined by an effective potential which depends on the density distribution of the condensate. We study the spectral properties for the situation of an isotropic harmonic and anharmonic as well as axially symmetric confinement. In the latter case an intriguing analogy with Rydberg atoms in magnetic fields is encountered

Collective quantum jumps of Rydberg atoms

We study an open quantum system of atoms with long-range Rydberg interaction, laser driving, and spontaneous emission. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. The jumps are inherently collective and in fact exist only for a large number of atoms. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden.Comment: 4 page