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New Journal of Physics

Photo-ionization in far-off-resonance optical lattices

R. M. Potvliege, Charles S. Adams

Published Aug 30, 2006• 22 citations
Publisher

Abstract

We calculate the ionization lifetime of rubidium atoms trapped in an intense light field as a function of wavelength and principal quantum number n . The ionization lifetimes of ground state atoms range from essentially infinite to less than one second, for example in a 532 nm laser field with intensity 10 6 W cm −2 . The ionization lifetime of Rydberg states can be extremely short, e.g. the lifetime of the 35d state in a CO 2 laser field with intensity 10 5 W cm −2 and wavelength 10.6 μm is of order 100 ns. These results have important implications for achieving long coherence times, and for entanglement schemes based on Rydberg excitation in far-detuned optical lattices. In particular, fast photo-ionization could seriously compromise the possible realization of quantum gates based on Rydberg excitation of alkali atoms in a CO 2 laser lattice.

DOI
10.1088/1367-2630/8/8/163

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Physical Review A•Sep 17, 2018•43 citations
We calculate the ionization lifetime of rubidium atoms trapped in an intense light field as a function of wavelength and principal quantum number n . The ionization lifetimes of ground state atoms range from essentially infinite to less than one second, for example in a 532 nm laser field with intensity 10 6 W cm −2 . The ionization lifetime of Rydberg states can be extremely short, e.g. the lifetime of the 35d state in a CO 2 laser field with intensity 10 5 W cm −2 and wavelength 10.6 μm is of order 100 ns. These results have important implications for achieving long coherence times, and for entanglement schemes based on Rydberg excitation in far-detuned optical lattices. In particular, fast photo-ionization could seriously compromise the possible realization of quantum gates based on Rydberg excitation of alkali atoms in a CO 2 laser lattice.
We develop a theoretical understanding of the trapping of divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wave functions. The optical potential is proportional to the ac Stark polarizability. We find that in the independent-particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usually employed free-electron polarizability, the Rydberg contribution depends both on the laser intensity profile and on the rotational symmetry of the total electronic wave function. We focus on the J=0J=0J=0 Rydberg states of Sr and evaluate the dynamic polarizabilities of the 5sns5sns5sns(1S0{}^{1}{S}_{0}1S0​) and 5snp5snp5snp(3P0{}^{3}{P}_{0}3P0​) Rydberg states. We specifically chose the Sr atom for its optical-lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states [5s25{s}^{2}5s2(1S0{}^{1}{S}_{0}1S0​) and 5s5p5s5p5s5p(3P0{}^{3}{P}_{0}3P0​)] and the J=0J=0J=0 Rydberg states [5sns5sns5sns(1S0{}^{1}{S}_{0}1S0​) and 5snp5snp5snp(3P0{}^{3}{P}_{0}3P0​)] vanishes. We tabulate these wavelengths as a function of the principal quantum number nnn of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\ensuremath{\sim}$1000 nm are ``universal'' as they do not depend on the principal quantum number nnn.
Summary form only given. Interactions between neutral atoms are generally weak, but exciting these atoms in a Rydberg state considerably enhances their interaction through a long-range dipole-dipole potential. An interesting application of this dipole-dipole interaction is the dipole blockade in Rydberg excitation. This effect offers exciting possibilities for manipulating quantum bits stored in a single collective excitations in mesoscopic ensembles, or for realizing scalable quantum logic gate. The dipole blockade effect has been demonstrated in atomic ensembles by different groups, and recently also with two independently trapped atoms, which shows the possibility of creating entangle states and quantum logic gates. To extend and continue these results with more atoms, a promising method is to use atoms trapped in an optical lattice in the Mott insulator phase. To excite atoms into a Rydberg state, and to control the interactions and the dipole blockade, a high resolution laser scheme is needed. We use a two-photon excitation scheme 5s1/2rarr 6p3/2rarr ns or nd. The first step, at 420 nm, is realized by doubling a MOPA laser, with the second step at ~ 1000 nm. Both lasers are locked to a Fabry-Perot cavity, and the total excitation bandwidth is less than 3 MHz. After the excitation into the Rydberg state, we apply a pulsed electric field to ionize and detect the Rydberg atoms with an ion detector. To characterize and improve the efficiency of our ion detection, we have explored the direct ionization of ultracold atoms in a magneto-optical trap, or in a Bose-Einstein condensate. This calibration will allows us to characterize precisely the Rydberg excitation and to monitor its time evolution. First results on the Rydberg excitation of ultracold atoms in dipole traps and optical lattices will be presented. The prospect for creating Rydberg excitations inside a Mott insulator will also be discussed.
Summary form only given. Laser-cooled atoms can be excited into Rydberg states to study Rydberg gases at high densities and low atomic velocities. Dense clouds of such atoms undergo virtually complete ionization when their density exceeds a critical value dependent on the principal quantum number n. We report a new regime in which the excited Rydberg population spontaneously evolves into long-lived high-l states, the lifetimes of which exceed the natural lifetimes of the initially excited Rydberg levels by two orders of magnitude. /sup 87/Rb atoms are collected and cooled to 50 /spl mu/K in a magneto optical trap (MOT), which is periodically turned off for 50 ms. 1 ms after the shutdown of the MOT the Rydberg atoms are created via a two-step excitation process using a 5 /spl mu/s long diode laser pulse.
We have measured the radiative lifetimes of ns, np and nd Rydberg states of rubidium in the range 28 < n < 45. To enable long-lived states to be measured, our experiment uses slow-moving Rb atoms in a magneto-optical trap (MOT). Two experimental techniques have been adopted to reduce random and systematic errors. First, a narrow-bandwidth pulsed laser is used to excite the target Rydberg state, resulting in minimal shot-to-shot variation in the initial state population. Second, we monitor the target state population as a function of time delay from the laser pulse using a short-duration, millimetre-wave pulse that is resonant with a one- or two-photon transition. We then selectively field ionize the monitor state, and detect the resulting electrons with a micro-channel plate. This signal is an accurate mirror of the target state population, and is uncontaminated by contributions from other states which are populated by black body radiation. Our results are generally consistent with other recent experimental results obtained using a less sensitive method, and are also in excellent agreement with theory.
A magic optical dipole trap (ODT) can confine atoms in the ground state and a highly excited state with the same light shifts, resulting in a long-range coherent lifetime between them, which plays an important role in high-fidelity quantum logic gates, multi-body physics and other quantum information. Here, we use a sum-over-states model to calculate the dynamic polarizabilities of the 6S1/2 ground state and 46S1/2 Rydberg state of Cs atoms and identify corresponding magic wavelengths and magic detunings for trapping the two states in the range of 900–1950 nm. Then, we analyze the robustness of the magic condition and the feasibility of the experimental operation. Furthermore, we estimate the trapping lifetime of Cs Rydberg atoms by considering different dissipation mechanisms, such as photon scattering and photoionization in the magic ODT. The photoexcitation and photoionization of Cs atoms under the action of three-step laser pulses are calculated by the rate equation. The presented results for magic-wavelength ODTs are of great significance for quantum information and quantum computing based on Rydberg atoms.
By confining atoms in a state-insensitive optical lattice, the lifetime of the ground-state--Rydberg coherence is increased to $\ensuremath{\ge}20\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$, an order of magnitude improvement over previous experiments using freely diffusing atoms. Using these enhanced lifetimes, we measure the so-called magic lattice wavelengths for Rb and use them to extract the $6{p}_{3/2}\text{\ensuremath{-}}n{s}_{1/2}$ reduced electric dipole matrix elements. Good agreement is found with values obtained using an effective one-electron potential for principal quantum numbers nnn between n=30n=30n=30 and n=70n=70n=70. We develop a theoretical model based on quantized motion to map out the ground-state--Rydberg coherence as a function of time that is in good agreement with the experimental results. The availability of long coherence times may present new opportunities for high-resolution spectroscopy and quantum information science.