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Physical Review A

Diatomic molecules in optical and microwave dipole traps

Marius Lysebo, Leif Veseth

Published Mar 11, 2011• 3 citations
Publisher

Abstract

The dipole forces on rotating diatomic molecules are worked out in detail for optical as well as microwave radiation fields. The objective is in particular to investigate how the dipole forces and potentials depend on the subtle internal structure of the molecule, with special emphasis on hyperfine and Zeeman states. Dipole potentials are obtained from computations of the real part of the complex molecular polarizability, whereas the imaginary part yields the scattering force. Numerical examples are presented for ${}^{23}{\mathrm{Na}}_{2}$ and OH for optical (laser) fields related to strong electronic transitions and for microwave fields for the \ensuremath{\Lambda} doubling in the OH ground state.

DOI
10.1103/physreva.83.033407

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The dipole forces on rotating diatomic molecules are worked out in detail for optical as well as microwave radiation fields. The objective is in particular to investigate how the dipole forces and potentials depend on the subtle internal structure of the molecule, with special emphasis on hyperfine and Zeeman states. Dipole potentials are obtained from computations of the real part of the complex molecular polarizability, whereas the imaginary part yields the scattering force. Numerical examples are presented for 23Na2{}^{23}{\mathrm{Na}}_{2}23Na2​ and OH for optical (laser) fields related to strong electronic transitions and for microwave fields for the \ensuremath{\Lambda} doubling in the OH ground state.
The properties of molecule-optical elements such as lenses or prisms based on the interaction of molecules with optical fields depend in a crucial way on the molecular quantum state and its alignment created by the optical field. Herein, we consider the effects of state-dependent alignment in estimating the optical dipole force acting on the molecules and, to this end, introduce an effective polarizability which takes proper account of molecular alignment and is directly related to the alignment-dependent optical dipole force. We illustrate the significance of including molecular alignment in the optical dipole force by a trajectory study that compares previously used approximations with the present approach. The trajectory simulations were carried out for an ensemble of linear molecules subject to either propagating or standing-wave optical fields for a range of temperatures and laser intensities. The results demonstrate that the alignment-dependent effective polarizability can serve to provide correct estimates of the optical dipole force, on which a state-selection method applicable to nonpolar molecules could be based. We note that an analogous analysis of the forces acting on polar molecules subject to an inhomogeneous static electric field reveals a similarly strong dependence on molecular orientation.
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.
Selection of state-insensitive or ``magic'' trapping conditions with ultracold atoms or molecules, where pairs of internal states experience identical trapping potentials, brings substantial benefits to precision measurements and quantum computing schemes. Working at such conditions could ensure that the detrimental effects of inevitable inhomogeneities across an ultracold sample are significantly reduced. However, this aspect of confinement remains unexplored for ultracold polar molecules. Here, we present means to control the ac Stark shift of rotational states of ultracold diatomic polar molecules, when subjected to both trapping laser light and an external electric field. We show that both the strength and relative orientation of the two fields influence the trapping potential. In particular, we predict ``magic electric field strengths'' and a ``magic angle,'' where the Stark shift is independent of the dc external field for certain rotational states of the molecule.
The realization of rovibrationally stable dense samples of ultracold diatomic molecules remains one of the main stepping stones to achieve the next slate of major goals in the field of atomic and molecular physics. Though obtaining diatomic alkali molecules was seen as a logical next step following the optical cooling of atoms, many of the possible applications currently under investigation extend beyond atomic and molecular physics. For example, spectroscopy of ultracold molecules can help in testing extensions of the Standard Model via the search for a permanent electric dipole moment of the electron (1; 2), or the energy difference between enantiomers of chiral molecules (3). Various molecular transitions can be utilized to track the time dependence of fundamental constants, including the fine structure constant and the proton to electron mass ratio (4). They also open the way for cold and ultracold chemistry, where the interacting species and products are in a coherent quantum superposition state (5) and reactions can happen via quantum tunneling. Dipolar ultracold quantum gases promise to show a plethora of new phenomena due to anisotropic long-range dipole-dipole interactions (6). Dipolar molecules in optical lattices can be employed as a quantum simulator of condensed matter systems, and they are predicted to demonstrate new quantum phases such as a dipolar crystal, supersolid, checkerboard and collapse phases (7; 8). Ultracold polar molecules also represent an attractive platform for quantum computation (9). They offer a variety of long-lived states for qubit encoding, including rotational, spin and hyperfine (if electronic and nuclear spins are non-zero), Λ and Ω-doublet states (10) and scalability to a large number of qubits. Polar molecules can be easily controlled by DC electric and magnetic fields, as well as bymicrowave and optical fields, allowing the design of various traps (11; 12). The main appeal of polar molecules for quantum information processing, however, comes from their permanent electric dipole moment, permitting them to interact via a long-range dipole-dipole interaction. The dipole-dipole interaction offers a tool to construct two-qubit gates, required for universal quantum computation (9; 13). Ultracold molecules in their ground vibrational state v = 0 (and even in specific rotational, hyperfine or Zeeman states) are required formany of these applications since they have a large permanent electric dipole moment and are stable with respect to collisions and spontaneous emission. Currently translationally ultracold (100 nK 1 mK) molecules are produced by magneto(14) and photo-association (15) techniques. In a typical photoassociation scheme, 3
We report on the optical polarizability of microwave-shielded ultracold NaCs molecules in an optical dipole trap. While dressing a pair of rotational states with a microwave field, we observe a marked dependence of the optical polarizability on the intensity and detuning of the dressing field. To precisely characterize differential energy shifts between dressed rotational states, we establish dressed-state spectroscopy. For strong dressing fields, we find that a magic rotational transition can be engineered and demonstrate its insensitivity to laser intensity fluctuations. The results of this Letter have direct relevance for evaporative cooling and the recent demonstration of molecular Bose-Einstein condensates [Bigagli et al., Nature (London) 631, 289 (2024)NATUAS0028-083610.1038/s41586-024-07492-z] and may open a door to precision microwave spectroscopy in interacting many-body systems of microwave-shielded molecules.
Abstract Molecules have vibrational, rotational, spin-orbit and hyperfine degrees of freedom or quantum states, each of which responds in a unique fashion to external electromagnetic radiation. The control over superpositions of these quantum states is key to coherent manipulation of molecules. For example, the better the coherence time the longer quantum simulations can last. The important quantity for controlling an ultracold molecule with laser light is its complex-valued molecular dynamic polarizability. Its real part determines the tweezer or trapping potential as felt by the molecule, while its imaginary part limits the coherence time. Here, our study shows that efficient trapping of a molecule in its vibrational ground state can be achieved by selecting a laser frequency with a detuning on the order of tens of GHz relative to an electric-dipole-forbidden molecular transition. Close proximity to this nearly forbidden transition allows to create a sufficiently deep trapping potential for multiple rotational states without sacrificing coherence times among these states from Raman and Rayleigh scattering. In fact, we demonstrate that magic trapping conditions for multiple rotational states of the ultracold 23Na87Rb polar molecule can be created.