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Physical Review A

Direct evidence of three-body interactions in a cold Rb85 Rydberg gas

Jianing Han

Published Nov 1, 2010• 16 citations

Abstract

Cold Rydberg atoms trapped in a magneto-optical trap (MOT) are not isolated and they interact through dipole-dipole and multipole-multipole interactions. First-order dipole-dipole interactions and van der Waals interactions between two atoms have been intensively studied. However, the facts that the first-order dipole-dipole interactions and van der Waals interactions show the same size of broadening [A. Reinhard, K. C. Younge, T. C. Liebisch, B. Knuffman, P. R. Berman, and G. Raithel, Phys. Rev. Lett. 100, 233201 (2008)] and there are transitions between two dimer states [S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Cote, E. E. Eyler, and P. L. Gould, Phys. Rev. Lett. 91, 183002 (2003); K. R. Overstreet, Arne Schwettmann, Jonathan Tallant, and James P. Shaffer, Phys. Rev. A 76, 011403(R) (2007)] cannot be explained by the two-atom picture. The purpose of this article is to show the few-body nature of a dense cold Rydberg gas by studying the molecular-state microwave spectra. Specifically, three-body energy levels have been calculated. Moreover, the transition from three-body energy levels to two-body coupled molecular energy levels and to isolated atomic energy levels as a function of the internuclear spacing is studied. Finally, single-body, two-body, and three-body interaction regions are estimated according to the experimental data. The results reported here provides useful information for plasma formation, further cooling, and superfluid formation.

DOI: 10.1103/physreva.82.052501

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Cold Rydberg atoms trapped in a magneto-optical trap (MOT) are not isolated and they interact through dipole-dipole and multipole-multipole interactions. First-order dipole-dipole interactions and van der Waals interactions between two atoms have been intensively studied. However, the facts that the first-order dipole-dipole interactions and van der Waals interactions show the same size of broadening [A. Reinhard, K. C. Younge, T. C. Liebisch, B. Knuffman, P. R. Berman, and G. Raithel, Phys. Rev. Lett. 100, 233201 (2008)] and there are transitions between two dimer states [S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Cote, E. E. Eyler, and P. L. Gould, Phys. Rev. Lett. 91, 183002 (2003); K. R. Overstreet, Arne Schwettmann, Jonathan Tallant, and James P. Shaffer, Phys. Rev. A 76, 011403(R) (2007)] cannot be explained by the two-atom picture. The purpose of this article is to show the few-body nature of a dense cold Rydberg gas by studying the molecular-state microwave spectra. Specifically, three-body energy levels have been calculated. Moreover, the transition from three-body energy levels to two-body coupled molecular energy levels and to isolated atomic energy levels as a function of the internuclear spacing is studied. Finally, single-body, two-body, and three-body interaction regions are estimated according to the experimental data. The results reported here provides useful information for plasma formation, further cooling, and superfluid formation.

Few-body interactions offer the opportunity to study the isolated atom to few-body coupled molecules, and to condensed matter transitions. Atoms in molecules and in condensed matters are coupled by different orders of multipole–multipole interactions, which all stem from different orders of approximations from coulomb interactions between multiple charges. The lowest order multipole–multipole interaction is the dipole–dipole interaction, which is proportional to the size of the dipole. In this article, we use Rydberg atoms, which have more than 1000 times greater electric dipoles than the ground state atoms, to study the van der Waals interaction between few bodies. In addition to the large dipoles, the kinetic energy of the atoms is significantly reduced by reducing the temperature, which makes these interactions stable and observable. Here, we report on the 2D and 3D few-body interaction potentials and possible ways of creating semistable molecules in such an ultracold Rydberg gas with a temperature of ≈100 nK. Although we use Rydberg atoms in this article, this calculation can be applied to other states too. The results reported here are useful for studying repulsive van der Waals interactions and creating ultracold molecules.

Charge-dipole interactions are very common interactions among atoms and molecules, especially materials that can emit light or contain free charges. The second-order charge-dipole interactions, proportional to 1 R 4 , are stronger than the second-order dipole-dipole interactions or van der Waals interactions, proportional to 1 R 6 , at longer distances. In reality, there is more than one atom or charge; therefore, we focus on few-body charge-dipole interactions, such as charge-dipole-dipole interactions. Laser cooling and trapping allow us to study such interactions with much higher precision. In this article, charge-dipole interactions will be investigated in cold gases. To increase the interaction strength, we excite the cold atoms to highly excited states, Rydberg states. Here, we treat one Rydberg atom as a dipole; the excited electron and the ion core are the two poles of an electric dipole. Specifically, we study charge-atom interactions in cold Rydberg gases. The laser-cooled lower level atoms were excited to highly excited states, and we scanned a microwave to look at the line shape of a particular transition between two Rydberg states. It has been shown that adding a charge can enhance atom-atom interactions under certain circumstances.

Previous resonant dipole-dipole energy-transfer experiments of cold Rydberg gases [Anderson et al., Phys. Rev. Lett. 80, 249 (1998); Mourachko et al., Phys. Rev. Lett. 80, 253 (1998)] have been interpreted as providing evidence of many-body, as opposed to purely binary, effects. Here we separate two-body and many-body interactions by introducing an additional Rydberg state, which does not participate directly in the energy-transfer process, but is strongly coupled to one of the final states. We observe broadening of the energy-transfer resonances due to this added Rydberg state, which clearly demonstrates the many-body nature of the dipole-dipole interactions in such a system.

The energy level spectrum of a many-body system containing two shared, collective Rydberg excitations is measured using cold atoms in an optical dipole trap. Two pairs of independently tunable laser pulses are employed to spectroscopically probe the spectrum in a double-resonance excitation scheme. Depending on the magnitude of an applied electric field, the Rydberg-atom interactions can vary from resonant dipole-dipole to attractive or repulsive van der Waals, leading to characteristic signatures in the measured spectra. Our results agree with theoretical estimates of the magnitude and sign of the interactions.

We have observed a density-dependent frequency shift of more than 4 MHz in a cold

{}^{85}

Rb Rydberg gas trapped in a magneto-optical trap. A one-dimensional linearly aligned four-body model is proposed to explain the experimental data, and the calculation matches the experimental data. The calculation also shows that if the energy detuning between the two coupled states, the

nsnsns(n+1)s

and

nsnsnpnp

states in this case, is small, the lowest level of the

nsnsnpnp

manifold has the maximum mixing probability, causing a frequency shift instead of line broadening. The results reported may be used for few-body blockade, Rydberg single-atom imaging, studying few-body to many-body transitions and interactions, and few-body ionization as well as quantum metrology.

Abstract : Research on interactions between quantum gases and impurities has become an active area of AMO. Here, two setups have been constructed and operated towards these goals. In the first, a metal tip (diameter 125 microns) is mounted close to a magneto-optic trap (MOT). Rydberg excitations are implanted in a cold-atom region (diameter about 10 microns, length about 50 microns). Interactions between the excitations cause excitation blockades, short- and medium-range order, as well as dynamics due to van-der-Waals interaction. All these topics were studied. The second setup is a double-trap system, in which magnetically trapped rubidium atom samples are prepared between 1 and 10 micro-Kelvin temperature and densities of about 1012 cm-3. Cold circular Rydberg atoms have been prepared and trapped. The dynamics of these highly dipolar atoms in the magnetic trap was studied, and collision-induced loss was observed and traced back to collisions between the long-lived circular atoms and cold ground state atoms. Novel D-type molecules between Rydberg and ground-state atoms were realized. These molecules are due to an attractive triplet s-wave low-energy electron scattering interaction. Five papers were published [two Phys. Rev. Lett, 2 Phys. Rev. A] and one submitted to PRL.