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arXiv:1206.6155 · Physical Review A

Phase diagram of Rydberg atoms in a nonequilibrium optical lattice

Jing Qian, Guangjiong Dong, Lu Zhou, Weiping Zhang

Published Jun 26, 2012• 33 citations
arXivHTMLPDF

Abstract

We study the quantum nonequilibrium dynamics of ultracold three-level atoms trapped in an optical lattice, which are excited to their Rydberg states via a two-photon excitation with non-negligible spontaneous emission. Rich quantum phases, including the uniform phase, the antiferromagnetic phase, and the oscillatory phase are identified. We map out the phase diagram and find these phases can be controlled by adjusting the ratio of intensity of the pump light to the control light and that of two-photon detuning to the Rydberg interaction strength. When the two-photon detuning is blueshifted and the latter ratio is less than 1, bistability exists among the phases. Actually, this ratio controls the Rydberg-blockade and Rydberg-antiblockade effects, thus, the phase transition in this system can be considered as a possible approach to study both effects.

DOI
10.1103/physreva.85.065401

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•Jan 1, 2016•0 citations
We study the quantum nonequilibrium dynamics of ultracold three-level atoms trapped in an optical lattice, which are excited to their Rydberg states via a two-photon excitation with non-negligible spontaneous emission. Rich quantum phases, including the uniform phase, the antiferromagnetic phase, and the oscillatory phase are identified. We map out the phase diagram and find these phases can be controlled by adjusting the ratio of intensity of the pump light to the control light and that of two-photon detuning to the Rydberg interaction strength. When the two-photon detuning is blueshifted and the latter ratio is less than 1, bistability exists among the phases. Actually, this ratio controls the Rydberg-blockade and Rydberg-antiblockade effects, thus, the phase transition in this system can be considered as a possible approach to study both effects.
We study a driven-dissipative system of atoms in the presence of laser excitation to a Rydberg state and spontaneous emission. The atoms interact via the blockade effect, whereby an atom in the Rydberg state shifts the Rydberg level of neighboring atoms. We use mean-field theory to study how the Rydberg population varies in space. As the laser frequency changes, there is a continuous transition between the uniform and antiferromagnetic phases. The nonequilibrium nature also leads to a novel oscillatory phase and bistability between the uniform and antiferromagnetic phases.
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.
Engineering quantum phases with spontaneously broken symmetries is a major goal of research in different fields. Trapped ultracold Rydberg-excited atoms in optical lattices are a promising platform for realizing quantum phases with broken lattice translational symmetry since they are interacting over distances larger than the lattice constant. Although numerous theoretical works on trapped Rydberg-excited gases have predicted such phases, in particular, density wave or supersolid phases, their experimental observation proves to be difficult due to challenges such as scattering processes and the limited experimentally achievable coupling strength. Most of these previous studies have focused on isotropically interacting gases dressed with Rydberg sss states, while the effect of anisotropic interactions due to Rydberg-excited ppp states in trapped quantum gases remains much less investigated. Additionally, it was shown that the excitation scheme used to excite Rydberg ppp states possesses advantages regarding achievable coupling strengths and limitation of scattering processes compared to its sss-state counterpart, which makes the investigation of Rydberg ppp-state dressed quantum gases even more interesting. In the present work we study the extended two-component Bose-Hubbard model, realized with a bosonic quantum gas with Rydberg-excited ppp states trapped in an optical lattice, within the Gutzwiller mean-field theory. We compute the ground-state phase diagram and investigate its different regimes. By comparison to the phase diagram of the isotropic case, we find the anisotropic interaction to be more advantageous for the observation of supersolid phases.
We develop a theoretical approach for the dynamics of Rydberg excitations in ultracold gases,with a realistically large number of atoms. We rely on the reduction of the single-atom Bloch equations to rate equations, which is possible under various experimentally relevant conditions. Here, we explicitly refer to a two-step excitation scheme. We discuss the conditions under which our approach is valid by comparing the results with the solution of the exact quantum master equation for two interacting atoms. Concerning the emergence of an excitation blockade in a Rydberg gas, our results are in qualitative agreement with experiment. Possible sources of quantitative discrepancy are carefully examined. Based on the two-step excitation scheme, we predict the occurrence of an antiblockade effect and propose possible ways to detect this excitation enhancement experimentally in an optical lattice, as well as in the gas phase.
Interaction between Rydberg atoms can significantly modify Rydberg excitation dynamics. Under a resonant driving field the Rydberg-Rydberg interaction in high-lying states can induce shifts in the atomic resonance such that a secondary Rydberg excitation becomes unlikely leading to the Rydberg blockade effect. In a related effect, off-resonant coupling of light to Rydberg states of atoms contributes to the Rydberg anti-blockade effect where the Rydberg interaction creates a resonant condition that promotes a secondary excitation in a Rydberg atomic gas. Here, we study the light-matter interaction and dynamics of off-resonant two-photon excitations and include two- and three-atom Rydberg interactions and their effect on excited state dynamics in an ensemble of cold atoms. In an experimentally-motivated regime, we find the optimal physical parameters such as Rabi frequencies, two-photon detuning, and pump duration to achieve significant enhancement in the probability of generating doubly-excited collective atomic states. This results in large auto-correlation values due to the Rydberg anti-blockade effect and makes this system a potential candidate for a high-purity two-photon Fock state source.
Rydberg atoms have experimentally interestingproperties such as strong long-range Van der Waals interactions and the dipole blockade effect. In optical lattices the blockade effect ensures that only one Rydberg excitation per site is allowed, effectively creating a Rydberg crystal. We theoretically show that it is also possible for a one-dimensional Rydberg crystal to spontaneously form in a random ensemble of atoms, e.g. a magneto-optical trap. This is done using an existing Monte Carlo model [1] to simulate the excitation dynamics inside the intersection of two lasers for a two-step excitation scheme. With a blue-detuned laser for the upper transition, the first Rydberg excitation will occur after a relatively long time. That first Rydberg atom will then seed further Rydberg excitations, as the blockade effect shifts atoms at a certain distance into resonance. If two dimensions of the laser intersection are smaller than the blockade radius, a one-dimensional Rydberg crystal will form.