Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0707.0985

Rotating molecules in optical lattices, alignment and monopole crystals

Holt, J. R., J. M. F. Gunn

Published Jul 6, 2007• 0 citations
arXivHTMLPDF

Abstract

The recent progress towards production of near-ground state quantum-degenerate molecules raises the issue of how such "small" molecules behave in an optical lattice. In this Letter we show that the coupling of the molecular orientation to the local electric field direction will provide severalnew phenomena. In the case where the lasers forming different crystallographic directions of the lattice are incoherent, the orientation of the molecules is conserved (for L = 1) and a novel form of anisotropic superfluidity can be expected. When the lasers are coherent, and the optical lattice is such that the splitting of the rotational levels is large compared to the centre of mass energies,an adiabaic description of the molecular orientation is appropriate. This leads to geometric vector potentials, pseudo-magnetic monopoles and a frustrated band structure with degenerate minima.

DOI
10.48550/arxiv.0707.0985

Related papers

Aligning and orienting molecules trapped in octahedral crystal fields

Toni Kiljunen, Burkhard Schmidt, Nikolaus Schwentner

The effect of external fields on directional states of a linear molecule trapped in a crystal field of octahedral symmetry is studied numerically. Adiabatic field-dressed energy levels are obtained by solving the time-independent Schr\"odinger equation for the rotational degrees of freedom of the confined molecule. In the absence of external fields, the internal octahedral crystal field serves to transform free-rotor states to angularly confined librational states of defined parity which arrange in near-degenerate sets of high multiplicity. Interaction of a linearly polarized, nonresonant laser field with the polarizability or of a static electric field with the dipole moment create alignment or orientation of the molecular axis, respectively. In the latter case, the combined effect of the internal (octahedral) and external static field is instrumental in creating orientation by coupling different tunneling states. Depending on the polarization direction of the external fields with respect to the symmetry axes provided by the crystal field, cooperative and competitive effects are distinguished. If the direction of the external field coincides with the minima of the crystal field, high degrees of alignment or orientation can be achieved for specific states, even for low field strengths. Otherwise, high efficiency of this mechanism is restricted to high fields and low temperatures. Strategies for an experimental realization are outlined.

Physical Review A•Nov 29, 2005•17 citations

Molecular Hubbard Hamiltonian: Field regimes and molecular species

Michael L. Wall, E. Bekaroglu, Lincoln D. Carr

The molecular Hubbard Hamiltonian (MHH) naturally arises for ultracold ground-state polar alkali-metal dimer molecules in optical lattices. We show that, unlike ultracold atoms, different molecules display different many-body phases due to intrinsic variances in molecular structure even when the molecular symmetry is the same. We also demonstrate a wide variety of experimental controls on ${}^{1}\ensuremath{\Sigma}$ molecules via external fields, including applied static electric and magnetic fields, an ac microwave field, and the polarization and strength of optical lattice beams. We provide explicit numerical calculations of the parameters of the MHH, including tunneling and direct and exchange dipole-dipole interaction energies, for the molecules ${}^{6}$Li${}^{133}$Cs, ${}^{23}$Na${}^{40}$K, ${}^{87}$Rb${}^{133}$Cs, ${}^{40}$K${}^{87}$Rb, and ${}^{6}$Li${}^{23}$Na in weak and strong applied electric fields. As case studies of many-body physics, we use infinite-size matrix product state methods to explore the quantum phase transitions from the superfluid phase to half-filled and third-filled crystalline phases in one dimension.

arXiv:1212.3042•Physical Review A•Aug 12, 2013•19 citations

Effect of molecular rotation on enantioseparation

Andreas Jacob, Klaus Hornberger

Recently, several laser schemes have been proposed to separate racemic mixtures of enantiomers by splitting a molecular beam into subbeams consisting of molecules of definite chirality [Y. Li, C. Bruder, and C. P. Sun, Phys. Rev. Lett. 99, 130403 (2007); X. Li and M. Shapiro, J. Chem. Phys. 132, 194315 (2010)]. These ideas rely on laser-induced effective gauge potentials in an adiabatic basis which lead to a chirality dependent force on the center-of-mass. However, the effect of molecular rotation has been neglected in these studies. Accounting for the full molecular quantum state we find that the potentials from the adiabatic dressed state approach cannot be recovered once the molecular orientation dynamics is included, even in the rotational ground state. This affects substantially the ability to perform enantioseparation in the above mentioned setups.

arXiv:1203.5684•The Journal of Chemical Physics•Jul 28, 2012•41 citations

Spin Superfluidity versus Solidity of Ultracold Polar Molecules

Hongyi Yu, Weijian Liu, Chaohong Lee

We present a technique for engineering quantum magnets via ultracold polar molecules in optical lattices and explore exotic interplay between its spin superfluidity and solidity. The molecular ground and first excited rotational states are resonantly coupled by a linearly polarized microwave field. The spin-up (spin-down) states are presented by molecular rotational states of electric dipole moment along (against) the coupling field. By controlling the angle between the lattice direction and the coupling field, the inter-site interaction can be tuned from antiferromagnetic to ferromagnetic. Furthermore, the dipole-dipole interaction induces an exotic interplay between spin superfluidity and solidity, and spin supersolid phases may appear in mediate regions.

arXiv:0910.4922•Oct 26, 2009•0 citations

Effect of rotational-state-dependent molecular alignment on the optical dipole force

Lee Yeong Kim, Ju Hyeon Lee, Hye Ah Kim +3 more

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.

arXiv:1606.00516•Physical Review A•Jul 27, 2016•6 citations

Polarization mixing in optical lattices with uniaxial anisotropy

Hashem Zoubi, Helmut Ritsch

We study resonant optical excitations of an ultracold gas in an optical lattice in the Mott insulator case. The particles possess anisotropy via an oriented optical transition dipole moment. The anisotropy, prepared by optical pumping into a certain Zeeman sublevel and/or by external static fields, is of a similar type as in uniaxial crystals. Between two mirrors the electronic excitations and the cavity photons of both TE and TM polarizations are coherently mixed to form polariton branches, which can directly be observed in the linear optical spectra. For example, for an incident field of TE polarization we obtain TE and TM transmitted and reflected fields. Also we calculate the phase shift in the TE and TM transmitted and reflected fields relative to the incident field phase, which leads to polarization rotations. Such polarization mixing can serve as a signature of the formation of oriented molecules from spherically symmetric atoms in optical lattices.

arXiv:0807.0761•Journal of Physics B Atomic Molecular and Optical Physics•Dec 12, 2008•5 citations
The recent progress towards production of near-ground state quantum-degenerate molecules raises the issue of how such "small" molecules behave in an optical lattice. In this Letter we show that the coupling of the molecular orientation to the local electric field direction will provide severalnew phenomena. In the case where the lasers forming different crystallographic directions of the lattice are incoherent, the orientation of the molecules is conserved (for L = 1) and a novel form of anisotropic superfluidity can be expected. When the lasers are coherent, and the optical lattice is such that the splitting of the rotational levels is large compared to the centre of mass energies,an adiabaic description of the molecular orientation is appropriate. This leads to geometric vector potentials, pseudo-magnetic monopoles and a frustrated band structure with degenerate minima.
The effect of external fields on directional states of a linear molecule trapped in a crystal field of octahedral symmetry is studied numerically. Adiabatic field-dressed energy levels are obtained by solving the time-independent Schr\"odinger equation for the rotational degrees of freedom of the confined molecule. In the absence of external fields, the internal octahedral crystal field serves to transform free-rotor states to angularly confined librational states of defined parity which arrange in near-degenerate sets of high multiplicity. Interaction of a linearly polarized, nonresonant laser field with the polarizability or of a static electric field with the dipole moment create alignment or orientation of the molecular axis, respectively. In the latter case, the combined effect of the internal (octahedral) and external static field is instrumental in creating orientation by coupling different tunneling states. Depending on the polarization direction of the external fields with respect to the symmetry axes provided by the crystal field, cooperative and competitive effects are distinguished. If the direction of the external field coincides with the minima of the crystal field, high degrees of alignment or orientation can be achieved for specific states, even for low field strengths. Otherwise, high efficiency of this mechanism is restricted to high fields and low temperatures. Strategies for an experimental realization are outlined.
The molecular Hubbard Hamiltonian (MHH) naturally arises for ultracold ground-state polar alkali-metal dimer molecules in optical lattices. We show that, unlike ultracold atoms, different molecules display different many-body phases due to intrinsic variances in molecular structure even when the molecular symmetry is the same. We also demonstrate a wide variety of experimental controls on ${}^{1}\ensuremath{\Sigma}$ molecules via external fields, including applied static electric and magnetic fields, an ac microwave field, and the polarization and strength of optical lattice beams. We provide explicit numerical calculations of the parameters of the MHH, including tunneling and direct and exchange dipole-dipole interaction energies, for the molecules 6{}^{6}6Li133{}^{133}133Cs, 23{}^{23}23Na40{}^{40}40K, 87{}^{87}87Rb133{}^{133}133Cs, 40{}^{40}40K87{}^{87}87Rb, and 6{}^{6}6Li23{}^{23}23Na in weak and strong applied electric fields. As case studies of many-body physics, we use infinite-size matrix product state methods to explore the quantum phase transitions from the superfluid phase to half-filled and third-filled crystalline phases in one dimension.
Recently, several laser schemes have been proposed to separate racemic mixtures of enantiomers by splitting a molecular beam into subbeams consisting of molecules of definite chirality [Y. Li, C. Bruder, and C. P. Sun, Phys. Rev. Lett. 99, 130403 (2007); X. Li and M. Shapiro, J. Chem. Phys. 132, 194315 (2010)]. These ideas rely on laser-induced effective gauge potentials in an adiabatic basis which lead to a chirality dependent force on the center-of-mass. However, the effect of molecular rotation has been neglected in these studies. Accounting for the full molecular quantum state we find that the potentials from the adiabatic dressed state approach cannot be recovered once the molecular orientation dynamics is included, even in the rotational ground state. This affects substantially the ability to perform enantioseparation in the above mentioned setups.
We present a technique for engineering quantum magnets via ultracold polar molecules in optical lattices and explore exotic interplay between its spin superfluidity and solidity. The molecular ground and first excited rotational states are resonantly coupled by a linearly polarized microwave field. The spin-up (spin-down) states are presented by molecular rotational states of electric dipole moment along (against) the coupling field. By controlling the angle between the lattice direction and the coupling field, the inter-site interaction can be tuned from antiferromagnetic to ferromagnetic. Furthermore, the dipole-dipole interaction induces an exotic interplay between spin superfluidity and solidity, and spin supersolid phases may appear in mediate regions.
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 study resonant optical excitations of an ultracold gas in an optical lattice in the Mott insulator case. The particles possess anisotropy via an oriented optical transition dipole moment. The anisotropy, prepared by optical pumping into a certain Zeeman sublevel and/or by external static fields, is of a similar type as in uniaxial crystals. Between two mirrors the electronic excitations and the cavity photons of both TE and TM polarizations are coherently mixed to form polariton branches, which can directly be observed in the linear optical spectra. For example, for an incident field of TE polarization we obtain TE and TM transmitted and reflected fields. Also we calculate the phase shift in the TE and TM transmitted and reflected fields relative to the incident field phase, which leads to polarization rotations. Such polarization mixing can serve as a signature of the formation of oriented molecules from spherically symmetric atoms in optical lattices.