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arXiv:quant-ph/0602017 · Physical Review A

Controlling polar molecules in optical lattices

Svetlana Kotochigova, Eite Tiesinga

Published Apr 17, 2006• 74 citations
arXivHTMLPDF

Abstract

We theoretically investigate the interaction of polar molecules with optical lattices and microwave fields. We demonstrate the existence of frequency windows in the optical domain where the complex internal structure of the molecule does not influence the trapping potential of the lattice. In such frequency windows the Franck-Condon factors are so small that near-resonant interaction of vibrational levels of the molecule with the lattice fields have a negligible contribution to the polarizability, and light-induced decoherences are kept to a minimum. In addition, we show that microwave fields can induce a tunable dipole-dipole interaction between ground-state rotationally symmetric $(J=0)$ molecules. A combination of a carefully chosen lattice frequency and microwave-controlled interaction between molecules will enable trapping of polar molecules in a lattice and possibly realize molecular quantum logic gates. Our results are based on ab initio relativistic electronic structure calculations of the polar KRb and RbCs molecules combined with calculations of their rovibrational motion.

DOI
10.1103/physreva.73.041405

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We theoretically investigate the interaction of polar molecules with optical lattices and microwave fields. We demonstrate the existence of frequency windows in the optical domain where the complex internal structure of the molecule does not influence the trapping potential of the lattice. In such frequency windows the Franck-Condon factors are so small that near-resonant interaction of vibrational levels of the molecule with the lattice fields have a negligible contribution to the polarizability, and light-induced decoherences are kept to a minimum. In addition, we show that microwave fields can induce a tunable dipole-dipole interaction between ground-state rotationally symmetric (J=0)(J=0)(J=0) molecules. A combination of a carefully chosen lattice frequency and microwave-controlled interaction between molecules will enable trapping of polar molecules in a lattice and possibly realize molecular quantum logic gates. Our results are based on ab initio relativistic electronic structure calculations of the polar KRb and RbCs molecules combined with calculations of their rovibrational motion.
The creation of a gas of ultracold polar molecules with a high phase space density brings new possibilities beyond experiments with ultracold atomic gases. In particular, long-range, anisotropic, and tunable dipole-dipole interactions open the way for novel quantum gases, with applications including strongly correlated many-body systems, and ultracold chemistry. This thesis will present the final steps to complete control over both internal and external degrees of freedom of the molecule which allows us to control, and even completely suppress, the chemical reactions between molecules. First, the control over internal states has been achieved through coherent state transfer to the ro-vibronic ground state and coherent manipulations of the hyperfine and rotational states with microwave radiation. Second, external degrees of freedom are controlled by loading the gas into an optical lattice. With the molecules loaded into a one-dimensional lattice, the orientation of the molecular collisions is controlled by manipulating both internal (hyperfine states) and external (motional states in the direction of tight confinement) degrees of freedom. Most striking is that by preparing the molecules all in the lowest band of the lattice in the same internal state, the molecular collisions can only occur in a side-by-side" orientation, where the chemical reaction rate is suppressed by the repulsive dipole-dipole interactions. The chemical reaction can be suppressed completely by further constraining the motion in the trap in a strong 3D lattice. Here we see lifetimes longer than 20 s, limited by o-resonant light scattering. Finally, the ac polarizability of the molecules is explored and controlled. The different rotational states of the molecule have different polarizabilities and will experience a different trapping force in both the optical dipole trap or lattice. We show that there is a magic angle" between the quantization axis and the polarization of the trapping laser at which the polarizabilities of two different rotational states can be matched, eliminating dephasing and allowing for coherent manipulations between rotational states.
We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar 23Na40K^{23}\mathrm{Na}^{40}\mathrm{K}23Na40K polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of 5.26(15)5.26(15)5.26(15) kV/cm and an angle of $54.{7}^{\ensuremath{\circ}}$ between this field and the polarization of the optical laser lead to a trapping design for 23Na40K^{23}\mathrm{Na}^{40}\mathrm{K}23Na40K molecules where decoherence due to electric field strength and laser-intensity fluctuations, as well as fluctuations in the direction of its polarization, are kept to a minimum. One-standard-deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions, pairs of hyperfine-rotational states of v=0v=0v=0 molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.
We determine conditions for effective quantum control over internal and external degrees of freedom of polar alkali-metal molecules in an optical trap. We calculate the dynamic molecular polarizability of KRb and RbCs as a function of laser frequency. The real part of the molecular polarizibility determines the depth of the trapping potential while the imaginary part contributes to laser-induced decoherences. Our results show that a relatively modest laser intensity is needed for strong confinement of polar molecules in an optical trap and that decoherence effects are manageable. More complete information on the scientific progress for the period of the extension is given in the Attachment.
We propose a mechanism to produce ultracold polar molecules with microwave fields. It converts trapped ultracold atoms into vibrationally excited molecules by a single microwave transition and entirely depends on the existence of a permanent dipole moment in the molecules. As opposed to production of molecules by photoassociation or magnetic-field Feshbach resonances, our method does not rely on properties of excited states or existence of Feshbach resonances. We determine conditions for optimal creation of polar molecules in vibrationally excited states of the ground-state potential by changing frequency and intensity of the microwave field. We also explore the possibility to produce vibrationally cold molecules by combining the microwave field with an optical Raman transition or by applying a microwave field to Feshbach molecules. The production mechanism is illustrated for KRb and RbCs.
We describe how to design a large class of always on spin-1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a ro-vibrational ground state molecule. Interactions are induced using a microwave field to mix ground states in one hyperfine manifold with the spin entangled dipole–dipole coupled excited states. Using multiple fields, anistropic models in one, two, or three dimensions can be built with tunable spatial range. An illustrative example in one-dimension is the generalized Haldane model, which at a specific parameter has a gapped valence bond solid ground state. The interaction strengths are large compared to decoherence rates and should allow for probing the rich phase structure of strongly correlated systems, including dimerized and gapped phases.
We study the possibility to use interaction between a polar molecule in the ground electronic and vibrational state and a Rydberg atom to construct two-qubit gates between molecular qubits and to coherently control molecular states. A polar molecule within the electron orbit in a Rydberg atom can either shift the Rydberg state, or form a Rydberg molecule. Both the atomic shift and the Rydberg molecule states depend on the initial internal state of the polar molecule, resulting in molecular state dependent van der Waals or dipole-dipole interaction between Rydberg atoms. Rydberg atoms mediated interaction between polar molecules can be enhanced up to 10(3) times. We describe how the coupling between a polar molecule and a Rydberg atom can be applied to coherently control molecular states, and specifically, to individually address molecules in an optical lattice, and to non-destructively readout molecular qubits.