Abstract

We demonstrate a novel experimental arrangement which can rotate a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, allowing investigation of phenomena such as the fractional quantum Hall effect. Our arrangement also allows the periodicity of a 2D optical lattice to be varied dynamically, producing a 2D accordion lattice.

© 2008 Optical Society of America

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References

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  1. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
    [CrossRef]
  2. J. K. Jain, Composite Fermions (OUP, 2007).
    [CrossRef]
  3. S. Viefers, “Quantum Hall physics in rotating Bose-Einstein condensates,” J. Phys.: Condens. Matter 20123202.1–123202.14 (2008)
    [CrossRef]
  4. A. S. Sorenson, E. Demler, and M. D. Lukin, “Fractional Quantum Hall States of Atoms in Optical Lattices,” Phys. Rev. Lett. 94, 086803 (2005)
    [CrossRef]
  5. R.N. Palmer and D. Jaksch, “High field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett. 96, 180407 (2006)
    [CrossRef] [PubMed]
  6. R. Bhat, M. Krämer, J. Cooper, and M. J. Holland, “Hall effects in Bose-Einstein condensates in a rotating optical lattice,” Phys. Rev. A 76, 043601 (2007)
    [CrossRef]
  7. D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56.1–56.11 (2003).
    [CrossRef]
  8. M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, “Realization of Fully Frustrated Josephson Junction Arrays with Cold Atoms,” Phys. Rev. Lett. 95, 010401 (2005)
    [CrossRef] [PubMed]
  9. K. Kasamatsu, “Uniformly frustrated bosonic Josephson junction arrays,” arXiv:0806.2012
  10. S. Tung, V. Schweikhard, and E. A. Cornell, “Observation of Vortex Pinning in Bose-Einstein Condensates,” Phys. Rev. Lett. 97, 240402 (2006)
    [CrossRef]
  11. K. Kasamatsu and M. Tsubota, “Dynamical vortex phases in a Bose-Einstein condensate driven by a rotating optical lattice,” Phys. Rev. Lett. 97, 240404 (2006)
    [CrossRef]
  12. “Optical Lattices and Quantum degenerate 87Rb in reduced dimensions,” John Howard Huckans, PhD thesis, University of Maryland (2006)
  13. L. Fallani, C. Fort, J. E. Lye, and M. Inguscio, “Bose-Einstein condensate in an optical lattice with tunable spacing: transport and static properties,” Opt. Express 13, 4303–4313 (2005)
    [CrossRef] [PubMed]
  14. T. C. Li, H. Kelkar, D. Medellin, and M. G. Raizen, “Real-time control of the periodicity of a standing wave: an optical accordion,” Opt. Express 16, 5465–5470 (2008)
    [CrossRef] [PubMed]
  15. M. Greiner, O. Mandel, T. Essingler, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator transition in a gas of ultracold atoms,” Nature 415, 39–44 (2002)
  16. D. Jaksch, “Optical Lattices, Ultracold Atoms and Quantum Information Processing,” Contemp. Phys. 45, 367–381 (2004).
    [CrossRef]
  17. B.E.A Saleh and M.C. Teich, Fundamentals of Photonics (Wiley, 1991) pp. 136–139
  18. M. Born and E. Wolf, Principles of Optics, 7th Edition (CUP, 1999) pp. 178–180
  19. N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap,” Nature 411, 1024–1027 (2001)
    [CrossRef] [PubMed]
  20. S. K. Schnelle, E. D. van Ooijen, M. J. Davis, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Versatile two-dimensional potentials for ultracold atoms,” Opt. Express 16, 1405–1412 (2008)
    [CrossRef] [PubMed]
  21. G. Milne, D. Rhodes, M. MacDonald, and K. Dholakia, “Fractionation of polydisperse colloid with acousto-optically generated potential energy landscapes,” Opt. Lett. 32, 1144–1146 (2007)
    [CrossRef] [PubMed]

2008 (3)

2007 (3)

G. Milne, D. Rhodes, M. MacDonald, and K. Dholakia, “Fractionation of polydisperse colloid with acousto-optically generated potential energy landscapes,” Opt. Lett. 32, 1144–1146 (2007)
[CrossRef] [PubMed]

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
[CrossRef]

R. Bhat, M. Krämer, J. Cooper, and M. J. Holland, “Hall effects in Bose-Einstein condensates in a rotating optical lattice,” Phys. Rev. A 76, 043601 (2007)
[CrossRef]

2006 (3)

S. Tung, V. Schweikhard, and E. A. Cornell, “Observation of Vortex Pinning in Bose-Einstein Condensates,” Phys. Rev. Lett. 97, 240402 (2006)
[CrossRef]

K. Kasamatsu and M. Tsubota, “Dynamical vortex phases in a Bose-Einstein condensate driven by a rotating optical lattice,” Phys. Rev. Lett. 97, 240404 (2006)
[CrossRef]

R.N. Palmer and D. Jaksch, “High field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett. 96, 180407 (2006)
[CrossRef] [PubMed]

2005 (3)

A. S. Sorenson, E. Demler, and M. D. Lukin, “Fractional Quantum Hall States of Atoms in Optical Lattices,” Phys. Rev. Lett. 94, 086803 (2005)
[CrossRef]

L. Fallani, C. Fort, J. E. Lye, and M. Inguscio, “Bose-Einstein condensate in an optical lattice with tunable spacing: transport and static properties,” Opt. Express 13, 4303–4313 (2005)
[CrossRef] [PubMed]

M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, “Realization of Fully Frustrated Josephson Junction Arrays with Cold Atoms,” Phys. Rev. Lett. 95, 010401 (2005)
[CrossRef] [PubMed]

2004 (1)

D. Jaksch, “Optical Lattices, Ultracold Atoms and Quantum Information Processing,” Contemp. Phys. 45, 367–381 (2004).
[CrossRef]

2003 (1)

D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56.1–56.11 (2003).
[CrossRef]

2002 (1)

M. Greiner, O. Mandel, T. Essingler, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator transition in a gas of ultracold atoms,” Nature 415, 39–44 (2002)

2001 (1)

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap,” Nature 411, 1024–1027 (2001)
[CrossRef] [PubMed]

Ahufinger, V.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
[CrossRef]

Bhat, R.

R. Bhat, M. Krämer, J. Cooper, and M. J. Holland, “Hall effects in Bose-Einstein condensates in a rotating optical lattice,” Phys. Rev. A 76, 043601 (2007)
[CrossRef]

Bloch, I.

M. Greiner, O. Mandel, T. Essingler, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator transition in a gas of ultracold atoms,” Nature 415, 39–44 (2002)

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th Edition (CUP, 1999) pp. 178–180

Cooper, J.

R. Bhat, M. Krämer, J. Cooper, and M. J. Holland, “Hall effects in Bose-Einstein condensates in a rotating optical lattice,” Phys. Rev. A 76, 043601 (2007)
[CrossRef]

Cornell, E. A.

S. Tung, V. Schweikhard, and E. A. Cornell, “Observation of Vortex Pinning in Bose-Einstein Condensates,” Phys. Rev. Lett. 97, 240402 (2006)
[CrossRef]

Damski, B.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
[CrossRef]

Davis, M. J.

Demler, E.

A. S. Sorenson, E. Demler, and M. D. Lukin, “Fractional Quantum Hall States of Atoms in Optical Lattices,” Phys. Rev. Lett. 94, 086803 (2005)
[CrossRef]

Dholakia, K.

Essingler, T.

M. Greiner, O. Mandel, T. Essingler, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator transition in a gas of ultracold atoms,” Nature 415, 39–44 (2002)

Fallani, L.

Fazio, R.

M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, “Realization of Fully Frustrated Josephson Junction Arrays with Cold Atoms,” Phys. Rev. Lett. 95, 010401 (2005)
[CrossRef] [PubMed]

Fort, C.

Grangier, P.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap,” Nature 411, 1024–1027 (2001)
[CrossRef] [PubMed]

Greiner, M.

M. Greiner, O. Mandel, T. Essingler, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator transition in a gas of ultracold atoms,” Nature 415, 39–44 (2002)

Hänsch, T. W.

M. Greiner, O. Mandel, T. Essingler, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator transition in a gas of ultracold atoms,” Nature 415, 39–44 (2002)

Heckenberg, N. R.

Holland, M. J.

R. Bhat, M. Krämer, J. Cooper, and M. J. Holland, “Hall effects in Bose-Einstein condensates in a rotating optical lattice,” Phys. Rev. A 76, 043601 (2007)
[CrossRef]

Inguscio, M.

Jain, J. K.

J. K. Jain, Composite Fermions (OUP, 2007).
[CrossRef]

Jaksch, D.

R.N. Palmer and D. Jaksch, “High field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett. 96, 180407 (2006)
[CrossRef] [PubMed]

D. Jaksch, “Optical Lattices, Ultracold Atoms and Quantum Information Processing,” Contemp. Phys. 45, 367–381 (2004).
[CrossRef]

D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56.1–56.11 (2003).
[CrossRef]

Kasamatsu, K.

K. Kasamatsu and M. Tsubota, “Dynamical vortex phases in a Bose-Einstein condensate driven by a rotating optical lattice,” Phys. Rev. Lett. 97, 240404 (2006)
[CrossRef]

K. Kasamatsu, “Uniformly frustrated bosonic Josephson junction arrays,” arXiv:0806.2012

Kelkar, H.

Krämer, M.

R. Bhat, M. Krämer, J. Cooper, and M. J. Holland, “Hall effects in Bose-Einstein condensates in a rotating optical lattice,” Phys. Rev. A 76, 043601 (2007)
[CrossRef]

Lewenstein, M.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
[CrossRef]

Li, T. C.

Lukin, M. D.

A. S. Sorenson, E. Demler, and M. D. Lukin, “Fractional Quantum Hall States of Atoms in Optical Lattices,” Phys. Rev. Lett. 94, 086803 (2005)
[CrossRef]

Lye, J. E.

MacDonald, A. H.

M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, “Realization of Fully Frustrated Josephson Junction Arrays with Cold Atoms,” Phys. Rev. Lett. 95, 010401 (2005)
[CrossRef] [PubMed]

MacDonald, M.

Mandel, O.

M. Greiner, O. Mandel, T. Essingler, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator transition in a gas of ultracold atoms,” Nature 415, 39–44 (2002)

Medellin, D.

Milne, G.

Palmer, R.N.

R.N. Palmer and D. Jaksch, “High field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett. 96, 180407 (2006)
[CrossRef] [PubMed]

Polini, M.

M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, “Realization of Fully Frustrated Josephson Junction Arrays with Cold Atoms,” Phys. Rev. Lett. 95, 010401 (2005)
[CrossRef] [PubMed]

Protsenko, I.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap,” Nature 411, 1024–1027 (2001)
[CrossRef] [PubMed]

Raizen, M. G.

Reymond, G.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap,” Nature 411, 1024–1027 (2001)
[CrossRef] [PubMed]

Rhodes, D.

Rubinsztein-Dunlop, H.

Saleh, B.E.A

B.E.A Saleh and M.C. Teich, Fundamentals of Photonics (Wiley, 1991) pp. 136–139

Sanpera, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
[CrossRef]

Schlosser, N.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap,” Nature 411, 1024–1027 (2001)
[CrossRef] [PubMed]

Schnelle, S. K.

Schweikhard, V.

S. Tung, V. Schweikhard, and E. A. Cornell, “Observation of Vortex Pinning in Bose-Einstein Condensates,” Phys. Rev. Lett. 97, 240402 (2006)
[CrossRef]

Sen, U.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
[CrossRef]

Sen(de), A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
[CrossRef]

Sorenson, A. S.

A. S. Sorenson, E. Demler, and M. D. Lukin, “Fractional Quantum Hall States of Atoms in Optical Lattices,” Phys. Rev. Lett. 94, 086803 (2005)
[CrossRef]

Teich, M.C.

B.E.A Saleh and M.C. Teich, Fundamentals of Photonics (Wiley, 1991) pp. 136–139

Tosi, M. P.

M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, “Realization of Fully Frustrated Josephson Junction Arrays with Cold Atoms,” Phys. Rev. Lett. 95, 010401 (2005)
[CrossRef] [PubMed]

Tsubota, M.

K. Kasamatsu and M. Tsubota, “Dynamical vortex phases in a Bose-Einstein condensate driven by a rotating optical lattice,” Phys. Rev. Lett. 97, 240404 (2006)
[CrossRef]

Tung, S.

S. Tung, V. Schweikhard, and E. A. Cornell, “Observation of Vortex Pinning in Bose-Einstein Condensates,” Phys. Rev. Lett. 97, 240402 (2006)
[CrossRef]

van Ooijen, E. D.

Viefers, S.

S. Viefers, “Quantum Hall physics in rotating Bose-Einstein condensates,” J. Phys.: Condens. Matter 20123202.1–123202.14 (2008)
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th Edition (CUP, 1999) pp. 178–180

Zoller, P.

D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56.1–56.11 (2003).
[CrossRef]

Adv. Phys. (1)

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, “Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007)
[CrossRef]

Contemp. Phys. (1)

D. Jaksch, “Optical Lattices, Ultracold Atoms and Quantum Information Processing,” Contemp. Phys. 45, 367–381 (2004).
[CrossRef]

J. Phys.: Condens. Matter (1)

S. Viefers, “Quantum Hall physics in rotating Bose-Einstein condensates,” J. Phys.: Condens. Matter 20123202.1–123202.14 (2008)
[CrossRef]

Nature (2)

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap,” Nature 411, 1024–1027 (2001)
[CrossRef] [PubMed]

M. Greiner, O. Mandel, T. Essingler, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator transition in a gas of ultracold atoms,” Nature 415, 39–44 (2002)

New J. Phys. (1)

D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56.1–56.11 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

R. Bhat, M. Krämer, J. Cooper, and M. J. Holland, “Hall effects in Bose-Einstein condensates in a rotating optical lattice,” Phys. Rev. A 76, 043601 (2007)
[CrossRef]

Phys. Rev. Lett. (5)

M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, “Realization of Fully Frustrated Josephson Junction Arrays with Cold Atoms,” Phys. Rev. Lett. 95, 010401 (2005)
[CrossRef] [PubMed]

S. Tung, V. Schweikhard, and E. A. Cornell, “Observation of Vortex Pinning in Bose-Einstein Condensates,” Phys. Rev. Lett. 97, 240402 (2006)
[CrossRef]

K. Kasamatsu and M. Tsubota, “Dynamical vortex phases in a Bose-Einstein condensate driven by a rotating optical lattice,” Phys. Rev. Lett. 97, 240404 (2006)
[CrossRef]

A. S. Sorenson, E. Demler, and M. D. Lukin, “Fractional Quantum Hall States of Atoms in Optical Lattices,” Phys. Rev. Lett. 94, 086803 (2005)
[CrossRef]

R.N. Palmer and D. Jaksch, “High field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett. 96, 180407 (2006)
[CrossRef] [PubMed]

Other (5)

J. K. Jain, Composite Fermions (OUP, 2007).
[CrossRef]

“Optical Lattices and Quantum degenerate 87Rb in reduced dimensions,” John Howard Huckans, PhD thesis, University of Maryland (2006)

K. Kasamatsu, “Uniformly frustrated bosonic Josephson junction arrays,” arXiv:0806.2012

B.E.A Saleh and M.C. Teich, Fundamentals of Photonics (Wiley, 1991) pp. 136–139

M. Born and E. Wolf, Principles of Optics, 7th Edition (CUP, 1999) pp. 178–180

Supplementary Material (2)

» Media 1: MOV (1851 KB)     
» Media 2: MOV (1889 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Two orthogonal standing wave intensity patterns in the focal plane of a lens combine to form a 2D lattice. The axial symmetry of the system allows rotation of the lattice to be realised.

Fig. 2.
Fig. 2.

Experimental arrangement for the generation of rotating interference fringes. BS is a non-polarising beam splitter cube, L1–L3 are converging lenses, M1 and M2 are mirrors.

Fig. 3.
Fig. 3.

It is convenient to describe the resultant intensity in the back focal plane of L3(z=F) in terms of the coordinates of the incident beams in the front focal plane of the lens (z=-F). The arrangement of Fig. 2 produced the second beam such that x 2(t)=-x 1(t), y 2(t)=-y 1(t), while x 1(t), y 1(t) were controlled by steering the laser beam with the AOD. D is the separation of the two beams incident on L3.

Fig. 4.
Fig. 4.

(a)–(c) Snapshots of the rotating lattice, taken while the lattice was rotating (Media 1). (d)–(f) Two dimensional Fourier transforms of Figs. (a)–(c) respectively. The red circle has been added to the images to highlight that the periodicity of the lattice was constant as the lattice rotated. The width of the peaks in the Fourier transforms represent the uncertainty in the lattice period, limited by the Fourier transform of the Gaussian envelope of the lattice. The lattice spacing is 104(4)µm and the 1/e 2 beam radius is 0.93mm.

Fig. 5.
Fig. 5.

(a)–(c) Implementing a two-dimensional optical accordion lattice: pictures of the optical lattice at different periodicities (Media 2). The lattice periodicities are: (a) 131(7)µm; (b) 87(3)µm; (c) 59(2)µm. The 1/e 2 beam radius is 0.93mm. The slight undulations that can be seen in the lattice are a result of wavefront aberration, and become less pronounced for smaller lattice spacings.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E ( r F , F ) = E 0 [ cos ( k 1 · r F ω t ) + cos ( k 2 · r F ω t ) ]
= 2 E 0 cos ( ( k 1 + k 2 ) . r F 2 ω t ) cos ( ( k 1 k 2 ) . r F 2 )
I ( r F , F ) = 2 I 0 [ 1 + cos ( k 1 k 2 ) · r F ] .
I ( x F , y F , F ) = 2 I 0 [ 1 + cos 2 π λ ( 2 x 1 x F + 2 y 1 y F F ) ] .
I ( x F , y F , F ) = 2 I 0 [ 1 + cos 2 π d ( x F cos Ω t + y F sin Ω t ) ]

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