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arXiv:1008.3856 · Physical Review A

Electric-field-dependent dynamic polarizability and state-insensitive conditions for optical trapping of diatomic polar molecules

Svetlana Kotochigova, David P. DeMille

Published Dec 30, 2010• 59 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.82.063421

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•Jan 1, 2024•0 citations
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.
We determine trapping conditions for ultracold polar molecules, where pairs of internal states experience identical trapping potentials. Such conditions could ensure that detrimental effects of inevitable inhomogeneities across an ultracold sample are significantly reduced. In particular, we investigate the internal rovibronic and hyperfine quantum states of ultracold fermionic ground-state 40K87Rb polar molecules, when static magnetic, static electric and trapping laser fields are simultaneously applied. Understanding the effect of changing the relative orientation or polarisation of these three fields is of crucial importance for the creation of decoherence-free subspaces built from two or more rovibronic states. Moreover, we evaluate the induced dipole moment of the molecule in the presence of these fields, which will allow control of interactions between molecules in different sites of an optical lattice, and study the influence of the interaction anisotropy on the ability to entangle polar molecules.
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.
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.
Abstract Ultracold molecules trapped in optical tweezers show great promise for the implementation of quantum technologies and precision measurements. We study a prototypical scenario where two interacting polar molecules placed in separate traps are controlled using an external electric field. This, for instance, enables a quantum computing scheme in which the rotational structure is used to encode the qubit states. We estimate the typical operation timescales needed for state engineering to be in the range of few microseconds. We further underline the important role of the spatial structure of the two-body states, with the potential for significant gate speedup employing trap-induced resonances.
Abstract Ultracold polar molecules combine a rich structure of long-lived internal states with access to controllable long-range anisotropic dipole–dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous differential light shifts. Here we demonstrate a rotationally magic optical trap for 87 Rb 133 Cs molecules that supports a Ramsey coherence time of 0.78(4) s in the absence of dipole–dipole interactions. This is estimated to extend to >1.4 s at the 95% confidence level using a single spin-echo pulse. In our trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation.
Ultracold polar molecules have become the subject of burgeoning fields of research in recent years owing to their prospects in quantum simulation, quantum computation and precision measurement. Their relatively large ground state dipole moment, coupled with a complex internal structure forms an incredibly powerful toolbox in which to perform quantum science experiments. Unfortunately, spatial confinement using light, which is necessary for many of the aforementioned applications, causes differential ac Stark shifts between quantum states, limiting coherence times and stifling their applicability. By accessing a so-called magic condition, this effect can be eliminated. This thesis presents work towards producing a quantum simulator based on a bulk gas of 87Rb133Cs molecules. We develop a magic wavelength trap by exploring nominally forbidden transitions from the X1Σ + ground state to b 3Π0 states. By tuning our trapping laser between transitions to different vibrational states of b3Π0, we can arbitrarily tune the difference in polarisability between pairs of rotational states and engineer second-scale coherence times. When we trap our molecules in a superposition of rotational states that exhibit a dipole moment in the laboratory frame, we observe the effects of long-range dipole-dipole interactions between molecules. These dipole-dipole interactions form the basis for quantum simulation and computation applications, observations of which marks an important milestone for realising a quantum simulator using 87Rb133Cs. We then demonstrate a route to ground state 87Rb133Cs molecules that is compatible with a protocol for loading Feshbach molecules into an optical lattice, developed by researchers at the University of Innsbruck. This method can be combined with a magic wavelength trap to produce a sample of 87Rb133Cs molecules in a magic lattice. Finally, we engineer synthetic dimensions that simulate simple single-particle Hamiltonians by coupling multiple rotational states in 87Rb133Cs. This forms the foundations for utilising rotational states of diatomic molecules as a platform for exploring synthetic dimensions