Abstract

A light beam tightly focused by a high numerical-aperture lens system contains longitudinal components with polarization parallel to the propagation axis. By numerically analyzing the polarization distribution around the focal region in one pair of confocally aligned counter-propagating tightly focused light beams with orthogonal linear polarizations, we found that there exists a three-dimensional polarization gradient pattern similar to that used in cooling neutral atoms. This can be used to three-dimensionally cool atoms trapped in a far-off-resonant trap with only one pair of counter-propagating beams in one dimension. This new cooling scheme can be used to individually cool single atoms in an addressable two-dimensional single-atom array for quantum information processing and be applied to perform readouts of qubit encoded in these atoms without losing them.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]

2015 (3)

Y. Minowa, R. Kawai, and M. Ashida, “Optical levitation of a microdroplet containing a single quantum dot,” Opt. Lett. 40(6), 906–909 (2015).
[Crossref] [PubMed]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

2014 (5)

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343(6178), 1493–1496 (2014).
[Crossref] [PubMed]

J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9(5), 358–364 (2014).
[Crossref] [PubMed]

J. Gieseler, M. Spasenović, L. Novotny, and R. Quidant, “Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle,” Phys. Rev. Lett. 112(10), 103603 (2014).
[Crossref] [PubMed]

Z.-H. Wang, G. Li, Y.-L. Tian, and T.-C. Zhang, “Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap,” Front. Phys. 9(5), 634–639 (2014).
[Crossref]

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

2013 (4)

L. P. Neukirch, J. Gieseler, R. Quidant, L. Novotny, and A. Nick Vamivakas, “Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond,” Opt. Lett. 38(16), 2976–2979 (2013).
[Crossref] [PubMed]

J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, “Coherence and Raman sideband cooling of a single atom in an optical tweezer,” Phys. Rev. Lett. 110(13), 133001 (2013).
[Crossref] [PubMed]

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

2012 (3)

A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a single atom in an optical tweezer to its quantum ground state,” Phys. Rev. X 2(4), 041014 (2012).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109(10), 103603 (2012).
[Crossref] [PubMed]

G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, “Crossed vortex bottle beam trap for single-atom qubits,” Opt. Lett. 37(5), 851–853 (2012).
[Crossref] [PubMed]

2011 (5)

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quantum Inform. Process. 10(6), 907–924 (2011).
[Crossref]

M. J. Gibbons, C. D. Hamley, C. Y. Shih, and M. S. Chapman, “Nondestructive fluorescent state detection of single neutral atom qubits,” Phys. Rev. Lett. 106(13), 133002 (2011).
[Crossref] [PubMed]

A. Fuhrmanek, R. Bourgain, Y. R. P. Sortais, and A. Browaeys, “Free-space lossless state detection of a single trapped atom,” Phys. Rev. Lett. 106(13), 133003 (2011).
[Crossref] [PubMed]

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7(7), 527–530 (2011).
[Crossref]

2010 (2)

2008 (2)

C. Tuchendler, A. M. Lance, A. Browaeys, Y. R. P. Sortais, and P. Grangier, “Energy distribution and cooling of a single atom in an optical tweezer,” Phys. Rev. A 78(3), 033425 (2008).
[Crossref]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

1989 (1)

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[Crossref]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Aiello, A.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

Ashida, M.

Ashkin, A.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Banzer, P.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

Bauer, T.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

Birkl, G.

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quantum Inform. Process. 10(6), 907–924 (2011).
[Crossref]

Bourgain, R.

A. Fuhrmanek, R. Bourgain, Y. R. P. Sortais, and A. Browaeys, “Free-space lossless state detection of a single trapped atom,” Phys. Rev. Lett. 106(13), 133003 (2011).
[Crossref] [PubMed]

Browaeys, A.

A. Fuhrmanek, R. Bourgain, Y. R. P. Sortais, and A. Browaeys, “Free-space lossless state detection of a single trapped atom,” Phys. Rev. Lett. 106(13), 133003 (2011).
[Crossref] [PubMed]

C. Tuchendler, A. M. Lance, A. Browaeys, Y. R. P. Sortais, and P. Grangier, “Energy distribution and cooling of a single atom in an optical tweezer,” Phys. Rev. A 78(3), 033425 (2008).
[Crossref]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Carr, A. W.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

Chapman, M. S.

M. J. Gibbons, C. D. Hamley, C. Y. Shih, and M. S. Chapman, “Nondestructive fluorescent state detection of single neutral atom qubits,” Phys. Rev. Lett. 106(13), 133002 (2011).
[Crossref] [PubMed]

Chavez, I.

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Cohen-Tannoudji, C.

Dalibard, J.

Dellago, C.

J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9(5), 358–364 (2014).
[Crossref] [PubMed]

Deutsch, B.

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109(10), 103603 (2012).
[Crossref] [PubMed]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Florin, E.-L.

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

Foss-Feig, M.

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

Fuhrmanek, A.

A. Fuhrmanek, R. Bourgain, Y. R. P. Sortais, and A. Browaeys, “Free-space lossless state detection of a single trapped atom,” Phys. Rev. Lett. 106(13), 133003 (2011).
[Crossref] [PubMed]

Gibbons, M. J.

M. J. Gibbons, C. D. Hamley, C. Y. Shih, and M. S. Chapman, “Nondestructive fluorescent state detection of single neutral atom qubits,” Phys. Rev. Lett. 106(13), 133002 (2011).
[Crossref] [PubMed]

Gieseler, J.

J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9(5), 358–364 (2014).
[Crossref] [PubMed]

J. Gieseler, M. Spasenović, L. Novotny, and R. Quidant, “Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle,” Phys. Rev. Lett. 112(10), 103603 (2014).
[Crossref] [PubMed]

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

L. P. Neukirch, J. Gieseler, R. Quidant, L. Novotny, and A. Nick Vamivakas, “Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond,” Opt. Lett. 38(16), 2976–2979 (2013).
[Crossref] [PubMed]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109(10), 103603 (2012).
[Crossref] [PubMed]

Grangier, P.

C. Tuchendler, A. M. Lance, A. Browaeys, Y. R. P. Sortais, and P. Grangier, “Energy distribution and cooling of a single atom in an optical tweezer,” Phys. Rev. A 78(3), 033425 (2008).
[Crossref]

Hamley, C. D.

M. J. Gibbons, C. D. Hamley, C. Y. Shih, and M. S. Chapman, “Nondestructive fluorescent state detection of single neutral atom qubits,” Phys. Rev. Lett. 106(13), 133002 (2011).
[Crossref] [PubMed]

Hazzard, K. R. A.

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

He, X.

Huang, R.

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

Isenhower, L.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, “Crossed vortex bottle beam trap for single-atom qubits,” Opt. Lett. 37(5), 851–853 (2012).
[Crossref] [PubMed]

Jeney, S.

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

Kaufman, A. M.

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a single atom in an optical tweezer to its quantum ground state,” Phys. Rev. X 2(4), 041014 (2012).
[Crossref]

Kawai, R.

Kheifets, S.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343(6178), 1493–1496 (2014).
[Crossref] [PubMed]

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7(7), 527–530 (2011).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328(5986), 1673–1675 (2010).
[Crossref] [PubMed]

Kruse, J.

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quantum Inform. Process. 10(6), 907–924 (2011).
[Crossref]

Lance, A. M.

C. Tuchendler, A. M. Lance, A. Browaeys, Y. R. P. Sortais, and P. Grangier, “Energy distribution and cooling of a single atom in an optical tweezer,” Phys. Rev. A 78(3), 033425 (2008).
[Crossref]

Lester, B. J.

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a single atom in an optical tweezer to its quantum ground state,” Phys. Rev. X 2(4), 041014 (2012).
[Crossref]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Li, G.

Z.-H. Wang, G. Li, Y.-L. Tian, and T.-C. Zhang, “Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap,” Front. Phys. 9(5), 634–639 (2014).
[Crossref]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, “Crossed vortex bottle beam trap for single-atom qubits,” Opt. Lett. 37(5), 851–853 (2012).
[Crossref] [PubMed]

Li, T.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343(6178), 1493–1496 (2014).
[Crossref] [PubMed]

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7(7), 527–530 (2011).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328(5986), 1673–1675 (2010).
[Crossref] [PubMed]

Lichtman, M.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

Lukic, B.

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

Lukin, M. D.

J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, “Coherence and Raman sideband cooling of a single atom in an optical tweezer,” Phys. Rev. Lett. 110(13), 133001 (2013).
[Crossref] [PubMed]

Maller, K.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, “Crossed vortex bottle beam trap for single-atom qubits,” Opt. Lett. 37(5), 851–853 (2012).
[Crossref] [PubMed]

Medellin, D.

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328(5986), 1673–1675 (2010).
[Crossref] [PubMed]

Melin, K.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343(6178), 1493–1496 (2014).
[Crossref] [PubMed]

Minowa, Y.

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Neugebauer, M.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

Neukirch, L. P.

Nick Vamivakas, A.

Novotny, L.

J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9(5), 358–364 (2014).
[Crossref] [PubMed]

J. Gieseler, M. Spasenović, L. Novotny, and R. Quidant, “Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle,” Phys. Rev. Lett. 112(10), 103603 (2014).
[Crossref] [PubMed]

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

L. P. Neukirch, J. Gieseler, R. Quidant, L. Novotny, and A. Nick Vamivakas, “Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond,” Opt. Lett. 38(16), 2976–2979 (2013).
[Crossref] [PubMed]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109(10), 103603 (2012).
[Crossref] [PubMed]

Piotrowicz, M. J.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Quidant, R.

J. Gieseler, M. Spasenović, L. Novotny, and R. Quidant, “Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle,” Phys. Rev. Lett. 112(10), 103603 (2014).
[Crossref] [PubMed]

J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9(5), 358–364 (2014).
[Crossref] [PubMed]

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

L. P. Neukirch, J. Gieseler, R. Quidant, L. Novotny, and A. Nick Vamivakas, “Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond,” Opt. Lett. 38(16), 2976–2979 (2013).
[Crossref] [PubMed]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109(10), 103603 (2012).
[Crossref] [PubMed]

Raizen, M. G.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343(6178), 1493–1496 (2014).
[Crossref] [PubMed]

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7(7), 527–530 (2011).
[Crossref]

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328(5986), 1673–1675 (2010).
[Crossref] [PubMed]

Regal, C. A.

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a single atom in an optical tweezer to its quantum ground state,” Phys. Rev. X 2(4), 041014 (2012).
[Crossref]

Rey, A. M.

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

Reynolds, C. M.

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Saffman, M.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, “Crossed vortex bottle beam trap for single-atom qubits,” Opt. Lett. 37(5), 851–853 (2012).
[Crossref] [PubMed]

Schlosser, M.

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quantum Inform. Process. 10(6), 907–924 (2011).
[Crossref]

Shih, C. Y.

M. J. Gibbons, C. D. Hamley, C. Y. Shih, and M. S. Chapman, “Nondestructive fluorescent state detection of single neutral atom qubits,” Phys. Rev. Lett. 106(13), 133002 (2011).
[Crossref] [PubMed]

Simha, A.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343(6178), 1493–1496 (2014).
[Crossref] [PubMed]

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Sortais, Y. R. P.

A. Fuhrmanek, R. Bourgain, Y. R. P. Sortais, and A. Browaeys, “Free-space lossless state detection of a single trapped atom,” Phys. Rev. Lett. 106(13), 133003 (2011).
[Crossref] [PubMed]

C. Tuchendler, A. M. Lance, A. Browaeys, Y. R. P. Sortais, and P. Grangier, “Energy distribution and cooling of a single atom in an optical tweezer,” Phys. Rev. A 78(3), 033425 (2008).
[Crossref]

Spasenovic, M.

J. Gieseler, M. Spasenović, L. Novotny, and R. Quidant, “Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle,” Phys. Rev. Lett. 112(10), 103603 (2014).
[Crossref] [PubMed]

Taute, K.

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

Thompson, J. D.

J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, “Coherence and Raman sideband cooling of a single atom in an optical tweezer,” Phys. Rev. Lett. 110(13), 133001 (2013).
[Crossref] [PubMed]

Tian, Y.-L.

Z.-H. Wang, G. Li, Y.-L. Tian, and T.-C. Zhang, “Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap,” Front. Phys. 9(5), 634–639 (2014).
[Crossref]

Tichelmann, S.

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quantum Inform. Process. 10(6), 907–924 (2011).
[Crossref]

Tiecke, T. G.

J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, “Coherence and Raman sideband cooling of a single atom in an optical tweezer,” Phys. Rev. Lett. 110(13), 133001 (2013).
[Crossref] [PubMed]

Tuchendler, C.

C. Tuchendler, A. M. Lance, A. Browaeys, Y. R. P. Sortais, and P. Grangier, “Energy distribution and cooling of a single atom in an optical tweezer,” Phys. Rev. A 78(3), 033425 (2008).
[Crossref]

Vuletic, V.

J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, “Coherence and Raman sideband cooling of a single atom in an optical tweezer,” Phys. Rev. Lett. 110(13), 133001 (2013).
[Crossref] [PubMed]

Wall, M. L.

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

Wang, J.

Wang, Z.-H.

Z.-H. Wang, G. Li, Y.-L. Tian, and T.-C. Zhang, “Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap,” Front. Phys. 9(5), 634–639 (2014).
[Crossref]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[Crossref]

Xia, T.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

Xu, P.

Zhan, M.

Zhang, S.

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, “Crossed vortex bottle beam trap for single-atom qubits,” Opt. Lett. 37(5), 851–853 (2012).
[Crossref] [PubMed]

Zhang, T.-C.

Z.-H. Wang, G. Li, Y.-L. Tian, and T.-C. Zhang, “Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap,” Front. Phys. 9(5), 634–639 (2014).
[Crossref]

Zibrov, A. S.

J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, “Coherence and Raman sideband cooling of a single atom in an optical tweezer,” Phys. Rev. Lett. 110(13), 133001 (2013).
[Crossref] [PubMed]

Annu. Rev. Biochem. (1)

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Front. Phys. (1)

Z.-H. Wang, G. Li, Y.-L. Tian, and T.-C. Zhang, “Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap,” Front. Phys. 9(5), 634–639 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Nanotechnol. (1)

J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9(5), 358–364 (2014).
[Crossref] [PubMed]

Nat. Phys. (3)

R. Huang, I. Chavez, K. Taute, B. Lukic, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011).
[Crossref]

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7(7), 527–530 (2011).
[Crossref]

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9(12), 806–810 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (2)

C. Tuchendler, A. M. Lance, A. Browaeys, Y. R. P. Sortais, and P. Grangier, “Energy distribution and cooling of a single atom in an optical tweezer,” Phys. Rev. A 78(3), 033425 (2008).
[Crossref]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “A two-dimensional lattice of blue detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88(1), 013420 (2013).
[Crossref]

Phys. Rev. Lett. (9)

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits,” Phys. Rev. Lett. 114(10), 100503 (2015).
[Crossref] [PubMed]

M. J. Gibbons, C. D. Hamley, C. Y. Shih, and M. S. Chapman, “Nondestructive fluorescent state detection of single neutral atom qubits,” Phys. Rev. Lett. 106(13), 133002 (2011).
[Crossref] [PubMed]

A. Fuhrmanek, R. Bourgain, Y. R. P. Sortais, and A. Browaeys, “Free-space lossless state detection of a single trapped atom,” Phys. Rev. Lett. 106(13), 133003 (2011).
[Crossref] [PubMed]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109(10), 103603 (2012).
[Crossref] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, “Coherence and Raman sideband cooling of a single atom in an optical tweezer,” Phys. Rev. Lett. 110(13), 133001 (2013).
[Crossref] [PubMed]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

J. Gieseler, M. Spasenović, L. Novotny, and R. Quidant, “Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle,” Phys. Rev. Lett. 112(10), 103603 (2014).
[Crossref] [PubMed]

Phys. Rev. X (1)

A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a single atom in an optical tweezer to its quantum ground state,” Phys. Rev. X 2(4), 041014 (2012).
[Crossref]

Proc. R. Soc. Lond. A Math. Phys. Sci. (2)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[Crossref]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Quantum Inform. Process. (1)

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quantum Inform. Process. 10(6), 907–924 (2011).
[Crossref]

Science (3)

A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, “Two-particle quantum interference in tunnel-coupled optical tweezers,” Science 345(6194), 306–309 (2014).
[Crossref] [PubMed]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328(5986), 1673–1675 (2010).
[Crossref] [PubMed]

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343(6178), 1493–1496 (2014).
[Crossref] [PubMed]

Other (1)

B. Richards, “Diffraction in systems of high relative aperture,” in Astronomical Optics and Related Subjects, Z. Kopal, ed. (North Holland Publishing Company, 1955), pp. 352–359.

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Figures (7)

Fig. 1
Fig. 1 Geometry of the Debye–Wolf integral
Fig. 2
Fig. 2 Amplitude and phase distributions for the transverse electric field components (Ex components, (a) and (b)) and longitudinal electric field components (Ez components, (c) and (d)) on the z-x plane around the focal point in a tightly focused beam with linear polarization. The figures are calculated based on parameter settings NA = 0.55, focal length f = 18 mm, input beam waist w0 = 10 mm and wavelength λ = 852 nm. Figures 4 and 5 below are based on the same parameters.
Fig. 3
Fig. 3 Scheme of atom cooling by a pair of confocally aligned counter-propagating tightly focused light beams (B1 and B2) with orthogonal linear polarizations. The FORT has a bigger trap size and overlaps with the tightly focused beam.
Fig. 4
Fig. 4 (a) The DOC distribution composed by E1x and E2y on the z-x plane. (b) The corresponding light shift of the ground state on the z axis when the atom interacts with the tightly focused beams. Here the green solid line and red dashed line are for state |g -1/2> and |g +1/2> and blue dash-dotted line is light shift for linear polarized beam and is for reference here. For simplification we consider atoms with level structure shown in the inset of (b). The region inside the dashed lines in (a) and the shaded area in (b) indicate position variance of a Cesium oscillator with temperature of 100 µK trapped in a size of 2µm FORT by 1064nm laser as descripted in the main text.
Fig. 5
Fig. 5 (a) DOC distribution composed by E1x and E2z on the z–x plane with phase delay of π/2 at the origin of the coordinate system. The black dashed vertical lines on the right side of z = 0 correspond sequentially to z = λ/8, λ/4, 3λ/8, λ/2, 5λ/8. (b) The DOC distribution in y–x plane at z = 0 in (a). (c) The light shift for the Cesium atom ground state F = 4 in the central region of the tightly focused beams; the lines correspond in sequentially to mF = −4 to mF = 4. The inset shows the corresponding light shift in the ground state with simple atomic state structure (inset of Fig. 4(b)) on the y axis when the atom interacts with the tightly focused beams, where the green solid line and red dashed line are for state |g +1/2> and |g -1/2>; the blue dash-dotted line is the light shift for a linear polarized beam given as reference. (d) The polarized angle distribution in the y–x plane at z = λ/8 in (a), where the composed field is linear polarized. (e) The polarized angle distribution along the y at x = 0 in (d). The region inside the dashed lines in (a), (b), (d) and the shaded area in (c) and (e) indicate the position variance of a Cesium oscillator with temperature of 100 µK and trap size of 2µm FORT by 1064 nm laser as described in the main text.
Fig. 6
Fig. 6 Normalized friction coefficients produced by lens systems with different NA numbers. The friction coefficients are normalized to the values in conventional PGC of free moving atoms by “lin lin” and “ σ + σ -” configurations with same parameters. Blue solid squares and red solid circles are corresponding to “ σ + σ -”and “lin lin” configurations, respectively. The NA numbers used for calculation in figure are 0.29, 0.4, 0.55, 0.75 and 0.9. All the data are calculated under the following parameters: lens aperture = 23.6 mm, incident Gaussian beam waist = 10 mm, beam wavelength = 852 nm, trapping frequency ω 0 = 2π × 40 kHz, atom temperature = 100 µK.
Fig. 7
Fig. 7 (a) Energy dissipation with time by “lin lin” configuration in current discussing tightly focused instance (red dashed line) and conventional PGC (green solid line). (b) Energy dissipation with time by “ σ + σ -” configuration in current discussing tightly focused instance (red dashed line) and conventional PGC (green solid line). All the lines are produced by using following parameters and relations: beam wavelength = 852 nm, detuning δ = −7Γ, trapping frequency ω 0 = 2π × 40 kHz and 1/ τ p = 2 Γ s 0/9 as shown in Ref [19].

Equations (11)

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E ( x , y , z ) = i k 2 π Ω a ( s x , s y ) s z exp [ i k ( s x x + s y y + s z z ) ] d s x d s y ,
q = 2 E 1 E 2 E 1 2 + E 2 2 sin Φ ,
U ( F , m F ) = α F E 2 + β F q g F m F E 2 ,
1 τ p = ( Γ 2 ) I / I s a t 1 + 4 ( Δ / Γ ) 2 + ( I / I s a t ) ,
E ( y , t ) = E 0 ( ε e i k e f f y + ε ' e i k e f f y ) exp ( i ω t ) + c . c . ,
f ( y , v ) = 2 3 k e f f δ s 0 sin ( 2 k e f f y ) cos ( 2 k e f f y ) + 2 k e f f v τ p sin ( 2 k e f f y ) 1 + 4 v 2 τ p 2 ,
f ( y , v ) = 2 3 k e f f δ s 0 ( 2 k e f f y ) + 4 3 k e f f 2 δ s 0 v τ p ( 2 k e f f y ) 2 .
α 1 = 4 3 k e f f 2 δ s 0 τ p ( 2 k e f f y ) 2 .
α ¯ 1 = 16 3 k e f f 4 δ s 0 τ p E m ω 0 2 .
α 2 = 120 17 δ Γ 5 Γ 2 + 4 δ 2 k e f f 2 ,
d E d t = α v 2 .

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