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arXiv:cond-mat/0609703 · Physical Review A

Coherent control of self-trapping of cold bosonic atoms

C. E. Creffield

Published Mar 29, 2007• 36 citations
arXivHTMLPDF

Abstract

We study the behavior of ultracold bosonic atoms held in an optical lattice. We first show how a self-trapping transition can be induced in the system either by increasing the number of atoms occupying a lattice site or by raising the interaction strength above a critical value. We then investigate how applying a periodic driving potential to the self-trapped state can be used to coherently control the emission of a precise number of correlated bosons from the trapping site. This allows the preparation and transport of entangled bosonic states, which are of great relevance to novel technologies such as quantum-information processing.

DOI
10.1103/physreva.75.031607

Related papers

Dynamical control of cold bosons using oscillating potentials

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The dynamics of cold bosonic atoms held in an optical lattice can be profoundly modified by using a periodic driving potential to induce the quantum interference effect termed "coherent destruction of tunneling". In this way the entanglement and localization of individual particles [1] can be very precisely controlled, pointing to the attractive possibility of using these systems for quantum information processing. This tunneling control also allows the effects of inter-particle interactions to be manipulated in a novel fashion, thereby giving precise control of the quantum phase transition [2] between the Mott insulator and the superfluid, and also providing a convenient means to manipulate the self-trapping effect [3].

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Controlled Generation of Coherent Matter Currents Using a Periodic Driving Field

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We study the effect of a strong, oscillating driving field on the dynamics of ultracold bosons held in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how the driving field can be used to produce and maintain a coherent atomic current by controlling the phase of the intersite tunneling processes. We investigate both the stroboscopic and time-averaged behavior using Floquet theory, and demonstrate that this procedure provides a stable and precise method of controlling coherent quantum systems.

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Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattice cases but is simple enough that it can be applied to spatially inhomogeneous lattice systems.

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Controlling the Directed Quantum Transport of Ultracold Atoms in an Optical Lattice with a Periodic Driving Field

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We propose a new method to control the directed quantum transport of ultracold atoms in a one-dimensional optical lattice. In this proposal, the effective tunneling between the neighboring sites can be adjusted via coherent destruction of tunneling by tuning the phase of the external field, instead of using the driving field intensity or the frequency, thus the directed quantum transport of ultracold atoms can be coherently controlled in a much easier manner. Our proposal overcomes the major drawback of the method used by Creffield et al. [ Phys. Rev. Lett. 99 (2007) 110501 ], and can be implemented, in principle, in any one-dimensional optical lattice. Some potential applications of the scheme are also discussed.

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Focus on Cold Atoms in Optical Lattices

Immanuel Bloch, P. Zoller

Imagine you could produce an artificial crystal for quantum matter, defect free and with complete control over the periodic crystal potential. The shape of the periodic potential, its depth and the interactions between the underlying particles could be changed at will and the particles could be moved around in a highly controlled way, at essentially zero temperature. This sounds almost too good to be true, but it is in fact what optical lattices have made possible for cold and ultracold atoms. How does this work? Neutral atoms can be trapped in the periodic intensity pattern of light, which is formed when two laser beams interfere. The varying light intensity creates a periodic potential landscape – the optical lattice – for the atoms via an AC-Stark shift interaction. Such optical lattices have recently turned into a major research field, especially with the advent of degenerate bosonic and fermionic quantum gases. There, the artificial crystal of light is used to create and investigate fundamental quantum phases of bosonic and fermionic many-body systems. One of the great advantages of these systems is that the physical behaviour of the atoms is usually perfectly described by a simple underlying Hamiltonian. They can thus can be used as a testbed for modern condensed matter theories with unique manipulation and control possibilities. Furthermore, novel and exotic many body quantum phases have also been predicted to be realizable in such 'quantum simulators as Richard P Feynman might have called them. Some of the most famous Hamiltonians that have been proposed in this respect include the Bose–Hubbard and Hubbard Hamiltonians for interacting bosons and fermions in periodic potentials, respectively. The physics within the Hubbard Hamiltonian is believed to contain an explanation for the origin of High- T c superconductivity, but so far even the exact phase diagram of this basic Hamiltonian is still under discussion after decades of theoretical research on this problem. Another research focus in this respect has been to use ultracold atoms in optical lattices for the investigation of quantum magnetism. Here the spin state of an atom does not have to be restricted to two possible values, as for electrons, but can cover several possible magnetic substates, yielding rich and novel quantum phases. In the latest proposals, it has also been shown how quantum spin models could be robustly and efficiently simulated with polar molecules trapped in optical lattices. Next to exploring the fundamental behaviour of quantum matter in periodic potentials, optical lattices have also shown to be very useful for the generation of ultracold molecules. 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The topics covered by the articles in this Focus Issue of New Journal of Physics reflect almost the whole breadth of topics discussed above and in fact the great interest in this field has required us to split off some of the articles to be published at a later date (still as part of this focus issue). We hope that you will find detailed new research results in this collection that are of interest to you and furthermore hope that the issue can increase the interest of the non-expert for this exciting and interdisciplinary research field. The articles below represent the first contributions and further additions will appear. Focus on Cold Atoms in Otical Lattices Contents Theory of Feshbach molecule formation in a dilute gas during a magnetic field ramp J E Williams, Nicolai Nygaard and Charles W Clark Dressed molecules in an optical lattice K B Gubbels, D B M Dickersheid and Henk T C Stoof Precision measurement of spin-dependent interaction strengths for spin-1 and spin-2 87 Rb atoms Artur Widera, Fabrice Gerbier, Simon Folling, Tatjana Gericke, Olaf Mandel and Immanuel Bloch The Fermi–Hubbard model at unitarity Evgeni Burovski, Nikolay Prokof'ev, B Svistunov and M Troyer Interaction broadening of wannier functions and mott transitions in atomic BEC Jinbin Li, Yue Yu, A M Dudarev and Qian Niu Hanbury Brown–Twiss interferometry for fractional and integer Mott phases Ana Maria Rey, I I Satija and Charles W Clark Quantum random walk with Rydberg atoms in an optical lattice Robin Cote, Alexander Russell, Edward E. Eyler and Phillip Gould Raman Spectroscopy of Mott insulator states in optical lattices P Blair Blakie Interacting Bose gases in quasi-one dimensional optical lattices M A Cazalilla, A F Ho and Thierry Giamarchi Long distance transport of ultracold atoms using a 1D optical lattice Stefan Schmid, Gregor Thalhammer, Klaus Winkler, Florian Lang and J H Denschlag Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms S R Clark and Dieter Jaksch Extended fermionization of 1D bosons in optical lattices Guido Pupillo, Ana Maria Rey, Carl J Williams and Charles W Clark One-dimensional description of a Bose–Einstein condensate in a rotating closed-loop waveguide Sylvain Schwartz, Marco Cozzini, Chiara Menotti, I Carusotto, Philippe Bouyer and Sandro Stringari Photo-ionization in far-off resonant optical lattices R M Potvliege and Charles S Adams Cooling toolbox for atoms in optical lattices Markus Popp, J J Garcia-Ripoll, K G Vollbrecht and J I Cirac Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle David Clement, A F Varon, J A Retter, L Sanchez-Palencia, Alain Aspect and P Bouyer Quantum dynamics, particle localization and instability of Mott states: the effect of fermion-boson conversion on Mott states Fei Zhou and Congjun Wu Off-diagonal correlations of lattice impenetrable bosons in one dimension D M Gangardt and Gora V Shlyapnikov Collective mode damping and viscosity in a 1D unitary Fermi gas Matthias Punk and W Zwerger Coherent matter waves emerging from Mott-insulators K Rodriguez, S R Manmana, Madrazo Marcos Rigol, R M Noack and A Muramatsu Phase-matched matter wave collisions in periodic potentials Klaus Moelmer Fermion pairing with spin-density imbalance in an optical lattice T Koponen, J Kinnunen, J-P Martikainen, L M Jensen and P Törmä Macroscopic superpositions of superfluid flows David W Hallwood, Keith Burnett and Jacob Dunningham Mean-field phase diagram of disordered bosons in a lattice at nonzero temperature K V Krutitsky, A Pelster and R Graham A primary noise thermometer for ultracold Bose gases R Gati, J Esteve, B Hemmerling, T B Ottenstein, J Appmeier, A Weller and M K Oberthaler Precision preparation of strings of trapped neutral atoms Y Miroshnychenko, W Alt, I Dotsenko, L Förster, M Khudaverdyan, A Rauschenbeutel and D Meschede Cold Fermi gases: a new perspective on spin-charge separation Corinna Kollath and Ulrich Schollwöck Analysis of localization phenomena in weakly interacting disordered lattice gases T Schulte, S Drenkelforth, J Kruse, R Tiemeyer, K Sacha, J Zakrzewski, M Lewenstein, W Ertmer and J J Arlt Localization and anomalous transport in a 1D soft boson optical lattice A K Tuchman, W Li, H Chien, S Dettmer and M A Kasevich Quantum switches and quantum memories for matter-wave lattice solitons V Ahufinger, A Mebrahtu, R Corbalán and A Sanpera Quantum noise analysis of spin systems realized with cold atoms Robert W Cherng and Eugene Demler Effective-range description of a Bose gas under strong one- or two-dimensional confinement Pascal Naidon, Eite Tiesinga, William F Mitchell and Paul S Julienne Dissipative dynamics of atomic Hubbard models coupled to a phonon bath: dark state cooling of atoms within a Bloch band of an optical lattice A Griessner, A J Daley, S R Clark, D Jaksch and P Zoller Inhomogeneous broadening of a Mott insulator spectrum V Guarrera, L Fallani, J E Lye, C Fort and M Inguscio Immanuel Bloch, Johannes Gutenberg-Universität, Mainz, Germany Peter Zoller, Universität Innsbruck, Austria

New Journal of Physics•Aug 30, 2006•16 citations

Self-Trapping of Bosons and Fermions in Optical Lattices

Dirk-Sören Lühmann, Kai Bongs, K. Sengstock +1 more

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.

arXiv:0711.2975•Physical Review Letters•Jul 31, 2008•71 citations
We study the behavior of ultracold bosonic atoms held in an optical lattice. We first show how a self-trapping transition can be induced in the system either by increasing the number of atoms occupying a lattice site or by raising the interaction strength above a critical value. We then investigate how applying a periodic driving potential to the self-trapped state can be used to coherently control the emission of a precise number of correlated bosons from the trapping site. This allows the preparation and transport of entangled bosonic states, which are of great relevance to novel technologies such as quantum-information processing.
The dynamics of cold bosonic atoms held in an optical lattice can be profoundly modified by using a periodic driving potential to induce the quantum interference effect termed "coherent destruction of tunneling". In this way the entanglement and localization of individual particles [1] can be very precisely controlled, pointing to the attractive possibility of using these systems for quantum information processing. This tunneling control also allows the effects of inter-particle interactions to be manipulated in a novel fashion, thereby giving precise control of the quantum phase transition [2] between the Mott insulator and the superfluid, and also providing a convenient means to manipulate the self-trapping effect [3].
We study the effect of a strong, oscillating driving field on the dynamics of ultracold bosons held in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how the driving field can be used to produce and maintain a coherent atomic current by controlling the phase of the intersite tunneling processes. We investigate both the stroboscopic and time-averaged behavior using Floquet theory, and demonstrate that this procedure provides a stable and precise method of controlling coherent quantum systems.
Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattice cases but is simple enough that it can be applied to spatially inhomogeneous lattice systems.
We propose a new method to control the directed quantum transport of ultracold atoms in a one-dimensional optical lattice. In this proposal, the effective tunneling between the neighboring sites can be adjusted via coherent destruction of tunneling by tuning the phase of the external field, instead of using the driving field intensity or the frequency, thus the directed quantum transport of ultracold atoms can be coherently controlled in a much easier manner. Our proposal overcomes the major drawback of the method used by Creffield et al. [ Phys. Rev. Lett. 99 (2007) 110501 ], and can be implemented, in principle, in any one-dimensional optical lattice. Some potential applications of the scheme are also discussed.
Imagine you could produce an artificial crystal for quantum matter, defect free and with complete control over the periodic crystal potential. The shape of the periodic potential, its depth and the interactions between the underlying particles could be changed at will and the particles could be moved around in a highly controlled way, at essentially zero temperature. This sounds almost too good to be true, but it is in fact what optical lattices have made possible for cold and ultracold atoms. How does this work? Neutral atoms can be trapped in the periodic intensity pattern of light, which is formed when two laser beams interfere. The varying light intensity creates a periodic potential landscape – the optical lattice – for the atoms via an AC-Stark shift interaction. Such optical lattices have recently turned into a major research field, especially with the advent of degenerate bosonic and fermionic quantum gases. There, the artificial crystal of light is used to create and investigate fundamental quantum phases of bosonic and fermionic many-body systems. One of the great advantages of these systems is that the physical behaviour of the atoms is usually perfectly described by a simple underlying Hamiltonian. They can thus can be used as a testbed for modern condensed matter theories with unique manipulation and control possibilities. Furthermore, novel and exotic many body quantum phases have also been predicted to be realizable in such 'quantum simulators as Richard P Feynman might have called them. Some of the most famous Hamiltonians that have been proposed in this respect include the Bose–Hubbard and Hubbard Hamiltonians for interacting bosons and fermions in periodic potentials, respectively. The physics within the Hubbard Hamiltonian is believed to contain an explanation for the origin of High- T c superconductivity, but so far even the exact phase diagram of this basic Hamiltonian is still under discussion after decades of theoretical research on this problem. Another research focus in this respect has been to use ultracold atoms in optical lattices for the investigation of quantum magnetism. Here the spin state of an atom does not have to be restricted to two possible values, as for electrons, but can cover several possible magnetic substates, yielding rich and novel quantum phases. In the latest proposals, it has also been shown how quantum spin models could be robustly and efficiently simulated with polar molecules trapped in optical lattices. Next to exploring the fundamental behaviour of quantum matter in periodic potentials, optical lattices have also shown to be very useful for the generation of ultracold molecules. Imagine for example having two atoms at each lattice site of an optical lattice. Then photoassociation or Feshbach resonances can be used to convert these atom pairs into stable molecules in a defined rotational-vibrational quantum state. One might consider such a coherent conversion of atoms into molecules to be the ultimate quantum limit that we can reach in the control over a 'chemical reaction'. Next to being micro-laboratories for molecular physics, optical lattices also play an important role in quantum information processing. Atoms localized in the nodes of the optical potential can be seen as a natural quantum register that opens powerful possibilities for quantum computing. In this Focus Issue, it is shown, for example, how atoms can be sorted with an arrangement of two crossed optical standing waves. The topics covered by the articles in this Focus Issue of New Journal of Physics reflect almost the whole breadth of topics discussed above and in fact the great interest in this field has required us to split off some of the articles to be published at a later date (still as part of this focus issue). We hope that you will find detailed new research results in this collection that are of interest to you and furthermore hope that the issue can increase the interest of the non-expert for this exciting and interdisciplinary research field. The articles below represent the first contributions and further additions will appear. Focus on Cold Atoms in Otical Lattices Contents Theory of Feshbach molecule formation in a dilute gas during a magnetic field ramp J E Williams, Nicolai Nygaard and Charles W Clark Dressed molecules in an optical lattice K B Gubbels, D B M Dickersheid and Henk T C Stoof Precision measurement of spin-dependent interaction strengths for spin-1 and spin-2 87 Rb atoms Artur Widera, Fabrice Gerbier, Simon Folling, Tatjana Gericke, Olaf Mandel and Immanuel Bloch The Fermi–Hubbard model at unitarity Evgeni Burovski, Nikolay Prokof'ev, B Svistunov and M Troyer Interaction broadening of wannier functions and mott transitions in atomic BEC Jinbin Li, Yue Yu, A M Dudarev and Qian Niu Hanbury Brown–Twiss interferometry for fractional and integer Mott phases Ana Maria Rey, I I Satija and Charles W Clark Quantum random walk with Rydberg atoms in an optical lattice Robin Cote, Alexander Russell, Edward E. Eyler and Phillip Gould Raman Spectroscopy of Mott insulator states in optical lattices P Blair Blakie Interacting Bose gases in quasi-one dimensional optical lattices M A Cazalilla, A F Ho and Thierry Giamarchi Long distance transport of ultracold atoms using a 1D optical lattice Stefan Schmid, Gregor Thalhammer, Klaus Winkler, Florian Lang and J H Denschlag Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms S R Clark and Dieter Jaksch Extended fermionization of 1D bosons in optical lattices Guido Pupillo, Ana Maria Rey, Carl J Williams and Charles W Clark One-dimensional description of a Bose–Einstein condensate in a rotating closed-loop waveguide Sylvain Schwartz, Marco Cozzini, Chiara Menotti, I Carusotto, Philippe Bouyer and Sandro Stringari Photo-ionization in far-off resonant optical lattices R M Potvliege and Charles S Adams Cooling toolbox for atoms in optical lattices Markus Popp, J J Garcia-Ripoll, K G Vollbrecht and J I Cirac Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle David Clement, A F Varon, J A Retter, L Sanchez-Palencia, Alain Aspect and P Bouyer Quantum dynamics, particle localization and instability of Mott states: the effect of fermion-boson conversion on Mott states Fei Zhou and Congjun Wu Off-diagonal correlations of lattice impenetrable bosons in one dimension D M Gangardt and Gora V Shlyapnikov Collective mode damping and viscosity in a 1D unitary Fermi gas Matthias Punk and W Zwerger Coherent matter waves emerging from Mott-insulators K Rodriguez, S R Manmana, Madrazo Marcos Rigol, R M Noack and A Muramatsu Phase-matched matter wave collisions in periodic potentials Klaus Moelmer Fermion pairing with spin-density imbalance in an optical lattice T Koponen, J Kinnunen, J-P Martikainen, L M Jensen and P Törmä Macroscopic superpositions of superfluid flows David W Hallwood, Keith Burnett and Jacob Dunningham Mean-field phase diagram of disordered bosons in a lattice at nonzero temperature K V Krutitsky, A Pelster and R Graham A primary noise thermometer for ultracold Bose gases R Gati, J Esteve, B Hemmerling, T B Ottenstein, J Appmeier, A Weller and M K Oberthaler Precision preparation of strings of trapped neutral atoms Y Miroshnychenko, W Alt, I Dotsenko, L Förster, M Khudaverdyan, A Rauschenbeutel and D Meschede Cold Fermi gases: a new perspective on spin-charge separation Corinna Kollath and Ulrich Schollwöck Analysis of localization phenomena in weakly interacting disordered lattice gases T Schulte, S Drenkelforth, J Kruse, R Tiemeyer, K Sacha, J Zakrzewski, M Lewenstein, W Ertmer and J J Arlt Localization and anomalous transport in a 1D soft boson optical lattice A K Tuchman, W Li, H Chien, S Dettmer and M A Kasevich Quantum switches and quantum memories for matter-wave lattice solitons V Ahufinger, A Mebrahtu, R Corbalán and A Sanpera Quantum noise analysis of spin systems realized with cold atoms Robert W Cherng and Eugene Demler Effective-range description of a Bose gas under strong one- or two-dimensional confinement Pascal Naidon, Eite Tiesinga, William F Mitchell and Paul S Julienne Dissipative dynamics of atomic Hubbard models coupled to a phonon bath: dark state cooling of atoms within a Bloch band of an optical lattice A Griessner, A J Daley, S R Clark, D Jaksch and P Zoller Inhomogeneous broadening of a Mott insulator spectrum V Guarrera, L Fallani, J E Lye, C Fort and M Inguscio Immanuel Bloch, Johannes Gutenberg-Universität, Mainz, Germany Peter Zoller, Universität Innsbruck, Austria
We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.