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Journal of Physics Conference Series

Progress toward ultracold chemistry: ultracold atomic and photonic collisions

Jesús Pérez‐Ríos, Maxence Lepers, Romain Véxiau, Nadia Bouloufa-Maafa, Olivier Dulieu

Published Apr 10, 2014• 6 citations
Publisher

Abstract

The dynamics of ultracold quantum gases composed of atoms or molecules with extremely low translational energy E t /k B << 1 millikelvin is dominated by the long-range mutual interactions between particles. Such studies require a detailed modelling of the atom-molecule or molecule-molecule long-range interactions inside the quantum gas with or without the presence of external fields. This paper focuses on two particular aspects relevant to ultracold chemistry: (i) The calculation of rates for photoassociation of a cold atom and a cold molecule to create ultracold excited trimers, based on the knowledge of the long-range interaction between the two species, showing that such rates are encouraging under the density and temperature conditions of a nearly degenerate quantum gas; (ii) The determination of the long-range interactions between two identical polar bialkali molecules in their rovibronic ground level in the presence of an electric field, showing the possibility for the formation of ultracold polar tetramers by stimulated emission.

DOI
10.1088/1742-6596/488/1/012031

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Ultracold polar molecular quantum gases promise to open new research directions ranging from the study of ultra-cold chemistry, precision measurements to novel quantum phase transitions. Based on the preparation of high-phase space density gases of polar KRb molecules [1–3], I will discuss the control of dipolar collisions and chemical reactions of polar molecules in a regime where quantum statistics, single scattering partial waves, and quantum threshold laws play a dominant role [4]. In particular, I will point out the crucial role of electric dipole-dipole interactions [5] and external confinement [6] in determining the chemical reaction rate. Finally, I will discuss prospects of reaching quantum degeneracy in bialkali samples of polar molecules and prospects for these systems as novel dipolar quantum many-body systems.

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Towards Ultracold Polar 6li40k Molecules

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CHAPTER 4. Long-range Interactions Between Ultracold Atoms and Molecules

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The term long-range interactions refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds of Bohr radii. The energies involved are much smaller than the usual chemical bond energies. However, they are comparable with the typical kinetic energies of particles in an ultracold gas (T ≪ 1 K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases sheds a new light on the well-established topic of long-range interactions, because (i) the interacting atoms and molecules can be prepared in a well-defined quantum (electronic, vibrational, rotational, fine or hyperfine), ground or excited level; and (ii) long-range interactions can be tailored at will using external electromagnetic fields. In this chapter, we present the essential concepts and mathematical relations to calculate long-range potential energies. We start by deriving the multipolar expansion of the electrostatic interaction energy between classical charge distributions, both in Cartesian coordinates for pedagogical purpose, and in spherical coordinates for practical use. Then we combine multipolar expansion and quantum perturbation theory, to obtain the general first- and second-order energy corrections, including the well-known van der Waals energy. We consider two central examples in the current context of ultracold gases: (i) a pair of alkali metal atoms and (ii) a pair of alkali metal heteronuclear diatomic molecules in the presence of an electric field. We highlight the key role of the total angular momenta of the interacting particles and of the complex, irrespective of their electronic or nuclear, orbital or spin nature.

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Long-range interactions between ultracold atoms and molecules

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Focus on Cold and Ultracold Molecules

Lincoln D. Carr, Jun Ye

Cold and ultracold molecules are the next wave of ultracold physics, giving rise to an exciting array of scientific opportunities, including many body physics for novel quantum phase transitions, new states of matter, and quantum information processing. Precision tests of fundamental physical laws benefit from the existence of molecular internal structure with exquisite control. The study of novel collision and reaction dynamics will open a new chapter of quantum chemistry. Cold molecules bring together researchers from a variety of fields, including atomic, molecular, and optical physics, chemistry and chemical physics, quantum information science and quantum simulations, condensed matter physics, nuclear physics, and astrophysics, a truly remarkable synergy of scientific explorations. For the past decade there have been steady advances in direct cooling techniques, from buffer-gas cooling to cold molecular beams to electro- and magneto-molecular decelerators. 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Whether directly or indirectly cooled, heteronuclear polar molecules offer distinct new features in comparison to cold atoms, while sharing all of their advantages (purity, high coherence, controllability, tunable interactions, no disorder, etc). First, they are more easily manipulated because of the strong response of their electric dipole moment to external electric fields, DC or AC. The electric dipole moment also creates the new aspect of long range interactions. Second, they have a rich internal structure, with vibrational and rotational states, fine or hyperfine structure, and Ω- or Λ-doublets. This internal structure allows for wonderful new possibilities in areas such as precision measurement and exquisite control of system dynamics. 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This sets the tone for the focus issue, namely, openness, innovation, and possibility, an emphasis for which New Journal of Physics , an open-access journal of the highest quality, is especially fitted. Focus on Cold and Ultracold Molecules Contents Cold and ultracold molecules: science, technology and applications Lincoln D Carr, David DeMille, Roman V Krems and Jun Ye Ultracold molecules: new probes on the variation of fundamental constants Cheng Chin, V V Flambaum and M G Kozlov Probing the unitarity limit at low laser intensities Philippe Pellegrini and Robin Côté Single-photon molecular cooling Edvardas Narevicius, S Travis Bannerman and Mark G Raizen Quantum simulations of extended Hubbard models with dipolar crystals M Ortner, A Micheli, G Pupillo and P Zoller Collisional and molecular spectroscopy in an ultracold Bose–Bose mixture G Thalhammer, G Barontini, J Catani, F Rabatti, C Weber, A Simoni, F Minardi and M Inguscio Multi-channel modelling of the formation of vibrationally cold polar KRb molecules Svetlana Kotochigova, Eite Tiesinga and Paul S Julienne Formation of ultracold, highly polar X 1 Σ + NaCs molecules C Haimberger, J Kleinert, P Zabawa, A Wakim and N P Bigelow Quantum polarization spectroscopy of correlations in attractive fermionic gases T Roscilde, M Rodríguez, K Eckert, O Romero-Isart, M Lewenstein, E Polzik and A Sanpera Inelastic semiclassical collisions in cold dipolar gases Michael Cavagnero and Catherine Newell Quasi-universal dipolar scattering in cold and ultracold gases J L Bohn, M Cavagnero and C Ticknor Stark deceleration of lithium hydride molecules S K Tokunaga, J M Dyne, E A Hinds and M R Tarbutt Molecular vibrational cooling by optical pumping with shaped femtosecond pulses D Sofikitis, S Weber, A Fioretti, R Horchani, M Allegrini, B Chatel, D Comparat and P Pillet Deeply bound ultracold molecules in an optical lattice Johann G Danzl, Manfred J Mark, Elmar Haller, Mattias Gustavsson, Russell Hart, Andreas Liem, Holger Zellmer and Hanns-Christoph Nägerl Toward the production of quantum degenerate bosonic polar molecules, 41 K 87 Rb K Aikawa, D Akamatsu, J Kobayashi, M Ueda, T Kishimoto and S Inouye Influence of a Feshbach resonance on the photoassociation of LiCs J Deiglmayr, P Pellegrini, A Grochola, M Repp, R Côté, O Dulieu, R Wester and M Weidemüller The kinematic cooling of molecules with laser-cooled atoms Ken Takase, Larry A Rahn, David W Chandler and Kevin E Strecker Coherent collapses of dipolar Bose–Einstein condensates for different trap geometries J Metz, T Lahaye, B Fröhlich, A Griesmaier, T Pfau, H Saito, Y Kawaguchi and M Ueda High-energy-resolution molecular beams for cold collision studies L P Parazzoli, N Fitch, D S Lobser and H J Lewandowski Collisional effects in the formation of cold guided beams of polar molecules M Motsch, C Sommer, M Zeppenfeld, L D van Buuren, P W H Pinkse and G Rempe Towards sympathetic cooling of large molecules: cold collisions between benzene and rare gas atoms P Barletta, J Tennyson and P F Barker Efficient formation of ground-state ultracold molecules via STIRAP from the continuum at a Feshbach resonance Elena Kuznetsova, Marko Gacesa, Philippe Pellegrini, Susanne F Yelin and Robin Côté Emergent timescales in entangled quantum dynamics of ultracold molecules in optical lattices M L Wall and L D Carr Rotational state resolved photodissociation spectroscopy of translationally and vibrationally cold MgH + ions: toward rotational cooling of molecular ions K Højbjerre, A K Hansen, P S Skyt, P F Staanum and M Drewsen Collective transverse cavity cooling of a dense molecular beam Thomas Salzburger and Helmut Ritsch A Stark decelerator on a chip Samuel A Meek, Horst Conrad and Gerard Meijer Deceleration of molecules by dipole force potential: a numerical simulation Susumu Kuma and Takamasa Momose Ultracold molecules: vehicles to scalable quantum information processing Kathy-Anne Brickman Soderberg, Nathan Gemelke and Cheng Chin Magnetic field modification of ultracold molecule–molecule collisions T V Tscherbul, Yu V Suleimanov, V Aquilanti and R V Krems Spectroscopy of 39 K 85 Rb triplet excited states using ultracold a 3 Σ + state molecules formed by photoassociation J T Kim, D Wang, E E Eyler, P L Gould and W C Stwalley Pumping vortex into a Bose–Einstein condensate of heteronuclear molecules Z F Xu, R Q Wang and L You Intense atomic and molecular beams via neon buffer-gas cooling David Patterson, Julia Rasmussen and John M Doyle Dynamical properties of dipolar Fermi gases T Sogo, L He, T Miyakawa, S Yi, H Lu and H Pu Collisions of bosonic ultracold polar molecules in microwave traps Alexander V Avdeenkov Cold TiO(X 3 Δ)–He collisions Mei-Ju Lu and Jonathan D Weinstein Investigation of dephasing rates in an interacting Rydberg gas U Raitzsch, R Heidemann, H Weimer, B Butscher, P Kollmann, R Löw, H P Büchler and T Pfau Impact of electric fields on highly excited rovibrational states of polar dimers Rosario González-Férez and Peter Schmelcher Phase transition from straight into twisted vortex lines in dipolar Bose–Einstein condensates M Klawunn and L Santos Stimulating the production of deeply bound RbCs molecules with laser pulses: the role of spin–orbit coupling in forming ultracold molecules Subhas Ghosal, Richard J Doyle, Christiane P Koch and Jeremy M Hutson Sensitive measurement of m p / m e variance using vibrational transition frequencies of cold molecules Masatoshi Kajita

New Journal of Physics•May 14, 2009•75 citations
The dynamics of ultracold quantum gases composed of atoms or molecules with extremely low translational energy E t /k B << 1 millikelvin is dominated by the long-range mutual interactions between particles. Such studies require a detailed modelling of the atom-molecule or molecule-molecule long-range interactions inside the quantum gas with or without the presence of external fields. This paper focuses on two particular aspects relevant to ultracold chemistry: (i) The calculation of rates for photoassociation of a cold atom and a cold molecule to create ultracold excited trimers, based on the knowledge of the long-range interaction between the two species, showing that such rates are encouraging under the density and temperature conditions of a nearly degenerate quantum gas; (ii) The determination of the long-range interactions between two identical polar bialkali molecules in their rovibronic ground level in the presence of an electric field, showing the possibility for the formation of ultracold polar tetramers by stimulated emission.
Ultracold polar molecular quantum gases promise to open new research directions ranging from the study of ultra-cold chemistry, precision measurements to novel quantum phase transitions. Based on the preparation of high-phase space density gases of polar KRb molecules [1–3], I will discuss the control of dipolar collisions and chemical reactions of polar molecules in a regime where quantum statistics, single scattering partial waves, and quantum threshold laws play a dominant role [4]. In particular, I will point out the crucial role of electric dipole-dipole interactions [5] and external confinement [6] in determining the chemical reaction rate. Finally, I will discuss prospects of reaching quantum degeneracy in bialkali samples of polar molecules and prospects for these systems as novel dipolar quantum many-body systems.
Due to their low temperature of less than a milliKelvin and their long-range anisotropic interactions, ultracold polar molecules offer promising applications for quantum computing, the measurement of fundamental constants and ultracold chemistry and may allow the realization of new forms of quantum matter. The diatomic molecule 6Li40K is an excellent candidate for their implementation due to its large electric dipole moment. In this book, the author presents the first steps towards the creation of ultracold polar 6Li40K molecules. He gives a detailed description of the construction of an experimental apparatus which prepares, at ultracold temperatures, a gas mixture of the species 6Li and 40K. He demonstrates the association of these fermionic atoms to ultracold bosonic excited 6Li40K* molecules by photoassociation. The molecules will have to be transferred to their rovibrational and electronic ground state in order to become stable and polar. Photoassociation spectroscopy has been performed to gain information about convenient transfer schemes. Finally the author presents a novel method for the manipulation of ultracold particles, which can be applied to polar 6Li40K molecules.
The term long-range interactions refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds of Bohr radii. The energies involved are much smaller than the usual chemical bond energies. However, they are comparable with the typical kinetic energies of particles in an ultracold gas (T ≪ 1 K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases sheds a new light on the well-established topic of long-range interactions, because (i) the interacting atoms and molecules can be prepared in a well-defined quantum (electronic, vibrational, rotational, fine or hyperfine), ground or excited level; and (ii) long-range interactions can be tailored at will using external electromagnetic fields. In this chapter, we present the essential concepts and mathematical relations to calculate long-range potential energies. We start by deriving the multipolar expansion of the electrostatic interaction energy between classical charge distributions, both in Cartesian coordinates for pedagogical purpose, and in spherical coordinates for practical use. Then we combine multipolar expansion and quantum perturbation theory, to obtain the general first- and second-order energy corrections, including the well-known van der Waals energy. We consider two central examples in the current context of ultracold gases: (i) a pair of alkali metal atoms and (ii) a pair of alkali metal heteronuclear diatomic molecules in the presence of an electric field. We highlight the key role of the total angular momenta of the interacting particles and of the complex, irrespective of their electronic or nuclear, orbital or spin nature.
The term "long-range interactions" refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds Bohr radii. The involved energies are much smaller than the usual chemical bond energies. However, they are comparable with the typical kinetic energies of particles in an ultracold gas (T≪1KT\ll 1KT≪1K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases shed a new light on the well-established topic of long-range interactions, because: (i) the interacting atoms and molecules can be prepared in a well-defined quantum (electronic, vibrational, rotational, fine or hyper-fine), ground or excited level; and (ii) long-range interactions can be tailored at will using external electromagnetic fields. In this chapter, we present the essential concepts and mathematical relations to calculate long-range potential energies. We start with deriving the multipolar expansion of the electrostatic interaction energy between classical charge distributions, both in Cartesian coordinates for pedagogical purpose, and in spherical coordinates for practical use. Then we combine multipolar expansion and quantum perturbation theory, to obtain the general first- and second-order energy corrections, including the well-known van der Waals energy. We consider two central examples in the current context of ultracold gases: (i) a pair of alkali-metal atoms and (ii) a pair of alkali-metal heteronuclear diatomic molecules submitted to an electric field. We highlight the key role of the total angular momenta of the interacting particles and of the complex, irrespective of their electronic or nuclear, orbital or spin nature.
The creation of ultracold molecules is currently limited to diatomic species. In this Letter, we present a theoretical description of the photoassociation of ultracold atoms and molecules to create ultracold excited triatomic molecules, thus being a novel example of a light-assisted ultracold chemical reaction. The calculation of the photoassociation rate of an ultracold Cs_{2} molecule in its rovibrational ground state with an ultracold Cs atom at frequencies close to its resonant excitation is reported, based on the solution of the quantum dynamics involving the atom-molecule long-range interactions and assuming a model potential for the short-range physics. The rate for the formation of excited Cs_{3} molecules is predicted to be comparable with currently observed atom-atom photoassociation rates. We formulate an experimental proposal to observe this process relying on the available techniques of optical lattices and standard photoassociation spectroscopy.
Cold and ultracold molecules are the next wave of ultracold physics, giving rise to an exciting array of scientific opportunities, including many body physics for novel quantum phase transitions, new states of matter, and quantum information processing. Precision tests of fundamental physical laws benefit from the existence of molecular internal structure with exquisite control. The study of novel collision and reaction dynamics will open a new chapter of quantum chemistry. Cold molecules bring together researchers from a variety of fields, including atomic, molecular, and optical physics, chemistry and chemical physics, quantum information science and quantum simulations, condensed matter physics, nuclear physics, and astrophysics, a truly remarkable synergy of scientific explorations. For the past decade there have been steady advances in direct cooling techniques, from buffer-gas cooling to cold molecular beams to electro- and magneto-molecular decelerators. These techniques have allowed a large variety of molecules to be cooled for pioneering studies. Recent amazing advances in experimental techniques combining the ultracold and the ultraprecise have furthermore brought molecules to the point of quantum degeneracy. These latter indirect cooling techniques magnetically associate atoms from a Bose–Einstein condensate and/or a quantum degenerate Fermi gas, transferring at 90% efficiency highly excited Fano–Feshbach molecules, which are on the order of 10 000 Bohr radii in size, to absolute ground state molecules just a few Bohr across. It was this latter advance, together with significant breakthroughs in internal state manipulations, which inspired us to coordinate this focus issue now, and is the reason why we say the next wave of ultracold physics has now arrived. Whether directly or indirectly cooled, heteronuclear polar molecules offer distinct new features in comparison to cold atoms, while sharing all of their advantages (purity, high coherence, controllability, tunable interactions, no disorder, etc). First, they are more easily manipulated because of the strong response of their electric dipole moment to external electric fields, DC or AC. The electric dipole moment also creates the new aspect of long range interactions. Second, they have a rich internal structure, with vibrational and rotational states, fine or hyperfine structure, and Ω- or Λ-doublets. This internal structure allows for wonderful new possibilities in areas such as precision measurement and exquisite control of system dynamics. Therefore, although this focus issue contains a few articles on homonuclear molecules, more complex molecules such as benzene, and even a contribution on atomic chromium, which has a significant magnetic dipole moment, our main focus is on the heteronuclear polar case. This focus issue explores both direct and indirect cooling of mainly polar molecules, and the theory to support and inspire these advances. Thirty-eight research groups have contributed original work, and there are two review articles to complement these advances: the first covers cold and ultracold molecules broadly from few body to many body physics, including foundational theory, the technology to make them, and their scientific applications. The second is on the search for time variation of fundamental constants. The former review, which is comprehensive in nature, concludes with a list of open questions. This sets the tone for the focus issue, namely, openness, innovation, and possibility, an emphasis for which New Journal of Physics , an open-access journal of the highest quality, is especially fitted. Focus on Cold and Ultracold Molecules Contents Cold and ultracold molecules: science, technology and applications Lincoln D Carr, David DeMille, Roman V Krems and Jun Ye Ultracold molecules: new probes on the variation of fundamental constants Cheng Chin, V V Flambaum and M G Kozlov Probing the unitarity limit at low laser intensities Philippe Pellegrini and Robin Côté Single-photon molecular cooling Edvardas Narevicius, S Travis Bannerman and Mark G Raizen Quantum simulations of extended Hubbard models with dipolar crystals M Ortner, A Micheli, G Pupillo and P Zoller Collisional and molecular spectroscopy in an ultracold Bose–Bose mixture G Thalhammer, G Barontini, J Catani, F Rabatti, C Weber, A Simoni, F Minardi and M Inguscio Multi-channel modelling of the formation of vibrationally cold polar KRb molecules Svetlana Kotochigova, Eite Tiesinga and Paul S Julienne Formation of ultracold, highly polar X 1 Σ + NaCs molecules C Haimberger, J Kleinert, P Zabawa, A Wakim and N P Bigelow Quantum polarization spectroscopy of correlations in attractive fermionic gases T Roscilde, M Rodríguez, K Eckert, O Romero-Isart, M Lewenstein, E Polzik and A Sanpera Inelastic semiclassical collisions in cold dipolar gases Michael Cavagnero and Catherine Newell Quasi-universal dipolar scattering in cold and ultracold gases J L Bohn, M Cavagnero and C Ticknor Stark deceleration of lithium hydride molecules S K Tokunaga, J M Dyne, E A Hinds and M R Tarbutt Molecular vibrational cooling by optical pumping with shaped femtosecond pulses D Sofikitis, S Weber, A Fioretti, R Horchani, M Allegrini, B Chatel, D Comparat and P Pillet Deeply bound ultracold molecules in an optical lattice Johann G Danzl, Manfred J Mark, Elmar Haller, Mattias Gustavsson, Russell Hart, Andreas Liem, Holger Zellmer and Hanns-Christoph Nägerl Toward the production of quantum degenerate bosonic polar molecules, 41 K 87 Rb K Aikawa, D Akamatsu, J Kobayashi, M Ueda, T Kishimoto and S Inouye Influence of a Feshbach resonance on the photoassociation of LiCs J Deiglmayr, P Pellegrini, A Grochola, M Repp, R Côté, O Dulieu, R Wester and M Weidemüller The kinematic cooling of molecules with laser-cooled atoms Ken Takase, Larry A Rahn, David W Chandler and Kevin E Strecker Coherent collapses of dipolar Bose–Einstein condensates for different trap geometries J Metz, T Lahaye, B Fröhlich, A Griesmaier, T Pfau, H Saito, Y Kawaguchi and M Ueda High-energy-resolution molecular beams for cold collision studies L P Parazzoli, N Fitch, D S Lobser and H J Lewandowski Collisional effects in the formation of cold guided beams of polar molecules M Motsch, C Sommer, M Zeppenfeld, L D van Buuren, P W H Pinkse and G Rempe Towards sympathetic cooling of large molecules: cold collisions between benzene and rare gas atoms P Barletta, J Tennyson and P F Barker Efficient formation of ground-state ultracold molecules via STIRAP from the continuum at a Feshbach resonance Elena Kuznetsova, Marko Gacesa, Philippe Pellegrini, Susanne F Yelin and Robin Côté Emergent timescales in entangled quantum dynamics of ultracold molecules in optical lattices M L Wall and L D Carr Rotational state resolved photodissociation spectroscopy of translationally and vibrationally cold MgH + ions: toward rotational cooling of molecular ions K Højbjerre, A K Hansen, P S Skyt, P F Staanum and M Drewsen Collective transverse cavity cooling of a dense molecular beam Thomas Salzburger and Helmut Ritsch A Stark decelerator on a chip Samuel A Meek, Horst Conrad and Gerard Meijer Deceleration of molecules by dipole force potential: a numerical simulation Susumu Kuma and Takamasa Momose Ultracold molecules: vehicles to scalable quantum information processing Kathy-Anne Brickman Soderberg, Nathan Gemelke and Cheng Chin Magnetic field modification of ultracold molecule–molecule collisions T V Tscherbul, Yu V Suleimanov, V Aquilanti and R V Krems Spectroscopy of 39 K 85 Rb triplet excited states using ultracold a 3 Σ + state molecules formed by photoassociation J T Kim, D Wang, E E Eyler, P L Gould and W C Stwalley Pumping vortex into a Bose–Einstein condensate of heteronuclear molecules Z F Xu, R Q Wang and L You Intense atomic and molecular beams via neon buffer-gas cooling David Patterson, Julia Rasmussen and John M Doyle Dynamical properties of dipolar Fermi gases T Sogo, L He, T Miyakawa, S Yi, H Lu and H Pu Collisions of bosonic ultracold polar molecules in microwave traps Alexander V Avdeenkov Cold TiO(X 3 Δ)–He collisions Mei-Ju Lu and Jonathan D Weinstein Investigation of dephasing rates in an interacting Rydberg gas U Raitzsch, R Heidemann, H Weimer, B Butscher, P Kollmann, R Löw, H P Büchler and T Pfau Impact of electric fields on highly excited rovibrational states of polar dimers Rosario González-Férez and Peter Schmelcher Phase transition from straight into twisted vortex lines in dipolar Bose–Einstein condensates M Klawunn and L Santos Stimulating the production of deeply bound RbCs molecules with laser pulses: the role of spin–orbit coupling in forming ultracold molecules Subhas Ghosal, Richard J Doyle, Christiane P Koch and Jeremy M Hutson Sensitive measurement of m p / m e variance using vibrational transition frequencies of cold molecules Masatoshi Kajita