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arXiv:0911.1427 · Physical Review Letters

Dynamical Crystallization in the Dipole Blockade of Ultracold Atoms

Thomas Pohl, Eugene Demler, Mikhail D. Lukin

Published Jan 27, 2010• 275 citations
arXivHTMLPDF

Abstract

We describe a method for controlling many-body states in extended ensembles of Rydberg atoms, forming crystalline structures during laser excitation of a frozen atomic gas. Specifically, we predict the existence of an excitation-number staircase in laser excitation of atomic ensembles into Rydberg states. It is shown that such ordered states can be selectively excited by chirped laser pulses, and, via quantum state transfer from atoms to light, be used to create crystalline photonic states.

DOI
10.1103/physrevlett.104.043002

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We describe a method for controlling many-body states in extended ensembles of Rydberg atoms, forming crystalline structures during laser excitation of a frozen atomic gas. Specifically, we predict the existence of an excitation-number staircase in laser excitation of atomic ensembles into Rydberg states. It is shown that such ordered states can be selectively excited by chirped laser pulses, and, via quantum state transfer from atoms to light, be used to create crystalline photonic states.
Ultracold atomic gases have been used extensively in recent years to realize textbook examples of condensed matter phenomena. Recently, phase transitions to ordered structures have been predicted for gases of highly excited, 'frozen' Rydberg atoms. Such Rydberg crystals are a model for dilute metallic solids with tunable lattice parameters, and provide access to a wide variety of fundamental phenomena. We investigate theoretically how such structures can be created in four distinct cold atomic systems, by using tailored laser-excitation in the presence of strong Rydberg-Rydberg interactions. We study in detail the experimental requirements and limitations for these systems, and characterize the basic properties of small crystalline Rydberg structures in one, two and three dimensions.
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.
The collective excitations in ensembles of dissipative, laser driven ultracold atoms exhibit crystal-like patterns, a many-body effect of the Rydberg blockade mechanism. These crystalline structures are revealed in an experiment from a postselection of configurations with fixed numbers of excitations. Here, we show that these subensembles can be well represented by ensembles of effective particles that interact via logarithmic pair potentials. This allows one to study the emergent patterns with a small number of effective particles to determine the phases of Rydberg crystals and to systematically study contributions from N-body terms.
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.
Crystalline structures of highly excited Rydberg atoms can be a model for dilute metallic solids with tunable parameters, and provide access to the regime of strongly coupled systems. In practice, crystal creation is made difficult by the 'Rydberg blockade', where one atom in the Rydberg state shifts the energy levels of its neighbours out of resonance with the excitation laser. In our experiment, we can spatially detect Rydberg atoms by a combination of field-ionization, and subsequent acceleration of the remaining ions onto a multi-channel plate. In this way, we were able to determine the blockade radius from measuring second-order correlations. We have also made small ordered Rydberg structures by optically imprinting local excitations in a disordered atomic gas using a spatial light modulator. With this diffractive optical element it is possible to control the intensity of light in the far ¿eld and create almost any desired intensity pattern. We found that a Rydberg system with a dissipative mechanism can be mapped onto a set of rate equations that describe a wireless computer network. In these networks neighbouring transmitters have a similar blockade effect on each other. For the Rydberg system, we used mathematical tools developed for wireless networks, and applied this to optically imprinted square lattices.
Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. For quantum magnets, Ising models with power-law interactions are among the most elementary systems that support such phases. These models can be implemented by laser coupling ensembles of ultracold atoms to Rydberg states. Here, we report on the experimental preparation of crystalline ground states of such spin systems. We observe a magnetization staircase as a function of the system size and show directly the emergence of crystalline states with vanishing susceptibility. Our results demonstrate the precise control of Rydberg many-body systems and may enable future studies of phase transitions and quantum correlations in interacting quantum magnets.