Скачать презентацию Long coherence times with dense trapped atoms collisional Скачать презентацию Long coherence times with dense trapped atoms collisional

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Long coherence times with dense trapped atoms collisional narrowing and dynamical decoupling Nir Davidson Long coherence times with dense trapped atoms collisional narrowing and dynamical decoupling Nir Davidson Yoav Sagi, Ido Almog, Rami Pugatch, Miri Brook (Kurizki group, Michael Aizenman) Weizmann Institute of Science, Israel

Why dense atomic ensembles? • Efficiency of quantum memories depends on optical depth • Why dense atomic ensembles? • Efficiency of quantum memories depends on optical depth • Strong nonlinearity per photon • Collective coupling to SC circuits • Unique model system!

Quantum memories 2010 - : Us, Kuzmich, Porto, Rosenbusch, Bloch …. Quantum memories 2010 - : Us, Kuzmich, Porto, Rosenbusch, Bloch ….

Experimental setup • Magneto optical trapping • Sisyphus cooling • Raman sideband cooling • Experimental setup • Magneto optical trapping • Sisyphus cooling • Raman sideband cooling • Evaporative cooling

Experimental setup • Magneto optical trapping • Sisyphus cooling • Raman sideband cooling • Experimental setup • Magneto optical trapping • Sisyphus cooling • Raman sideband cooling • Evaporative cooling

Experimental setup • Magneto optical trapping • Sisyphus cooling • Raman sideband cooling • Experimental setup • Magneto optical trapping • Sisyphus cooling • Raman sideband cooling • Evaporative cooling

Experimental setup • Magneto optical trapping • Sisyphus cooling • Raman sideband cooling • Experimental setup • Magneto optical trapping • Sisyphus cooling • Raman sideband cooling • Evaporative cooling

Outline • Collisional narrowing • Spectrum with discrete fluctuations • Motional broadening • Dynamical Outline • Collisional narrowing • Spectrum with discrete fluctuations • Motional broadening • Dynamical decoupling • Bath spectral characterization

Motional narrowing “ ” Motional narrowing “ ”

Collisional narrowing Gaussian Exponent Collisional narrowing Gaussian Exponent

Experimental results Collisional narrowed decay time Y. Sagi, I. Almog and N. Davidson, Phys. Experimental results Collisional narrowed decay time Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 (2010) Inhomogeneous decay time

Experimental results Data collapse! Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. Experimental results Data collapse! Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 (2010)

Mott insulator suppresses collisions • Mott-Insulator atom per site with exactly one • ~80 Mott insulator suppresses collisions • Mott-Insulator atom per site with exactly one • ~80 Hz EIT lines • ~250 msec storage time for light U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, PRL 2010

Discrete Vs continuous fluctuations Kubo-Anderson model • Y. Sagi, R. Pugatch, I. Almog and Discrete Vs continuous fluctuations Kubo-Anderson model • Y. Sagi, R. Pugatch, I. Almog and N. Davidson, Phys. Rev. Lett. 104, 253003 (2010)

Discrete Vs continuous fluctuations Kubo-Anderson model • Cold collisions in atomic ensembles • Y. Discrete Vs continuous fluctuations Kubo-Anderson model • Cold collisions in atomic ensembles • Y. Sagi, R. Pugatch, I. Almog and N. Davidson, Phys. Rev. Lett. 104, 253003 (2010)

Discrete fluctuations • Telegraph noise in semiconductors • Single molecule spectroscopy Discrete fluctuations • Telegraph noise in semiconductors • Single molecule spectroscopy

Solution of the discrete model Without collisions: With collisions: A. Brissaud and U. Frisch, Solution of the discrete model Without collisions: With collisions: A. Brissaud and U. Frisch, J. Math. Phys. 15, 524 (1974).

Atoms in 3 D harmonic trap Density of states for 3 D harmonic trap Atoms in 3 D harmonic trap Density of states for 3 D harmonic trap Boltzmann factor

How do we measure the parameters? • t 1 is measured in low density How do we measure the parameters? • t 1 is measured in low density with

• G is measured by inducing oscillations in the waist of the atomic • G is measured by inducing oscillations in the waist of the atomic cloud and observing their decay:

Comparing theory to experiment Y. Sagi, R. Pugatch, I. Almog and N. Davidson, Phys. Comparing theory to experiment Y. Sagi, R. Pugatch, I. Almog and N. Davidson, Phys. Rev. Lett. 104, 253003 (2010)

Comparison to Kubo’s model Bloembergen et al, PRA 1984 Comparison to Kubo’s model Bloembergen et al, PRA 1984

Can fluctuations broaden the spectrum ? Example: Student’s t-distribution Motional narrowing A. Burnstein, Chem. Can fluctuations broaden the spectrum ? Example: Student’s t-distribution Motional narrowing A. Burnstein, Chem. Phys. Lett. 83, 335 (1981).

Can fluctuations broaden the spectrum ? Example: Student’s t-distribution Motional broadening A. Burnstein, Chem. Can fluctuations broaden the spectrum ? Example: Student’s t-distribution Motional broadening A. Burnstein, Chem. Phys. Lett. 83, 335 (1981). Motional narrowing

Can fluctuations broaden the spectrum ? Y. Sagi, I. Almog, R. Pugatch, M. Aizenman Can fluctuations broaden the spectrum ? Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Davidson, PRA, in press (2011)

Mathematical proof for stable distributions where α - characteristic exponent of a stable distribution Mathematical proof for stable distributions where α - characteristic exponent of a stable distribution Gaussian: α=2, Cauchy: α=1, Levi: α=1/2 Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Davidson, PRA, in press (2011)

Motional broadening: exponential decay Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Motional broadening: exponential decay Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Davidson, PRA, in press (2011)

Effect of cutoff Motional broadening persists until cutoff is sampled Effect of cutoff Motional broadening persists until cutoff is sampled

Relation to Zeno and anti Zeno Y. Sagi, I. Almog, R. Pugatch, M. Aizenman Relation to Zeno and anti Zeno Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Davidson, PRA, in press (2011)

Suppression of collisional decoherence by dynamical decoupling Suppression of collisional decoherence by dynamical decoupling

Echo fails at high densities Echo fails at high densities

Dynamical Decoupling Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 Dynamical Decoupling Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 (2010)

Process tomography of DD Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. Process tomography of DD Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 (2010)

Process tomography of non-linear Hamiltonian “twist” of the Bloch sphere Rubidium 87: a 11+a Process tomography of non-linear Hamiltonian “twist” of the Bloch sphere Rubidium 87: a 11+a 22 -2*a 12 = 0. 3% of a 11 and a 22

Measuring the bath spectrum S(w) F(w, t) W w Continuous Rabi pulse The decay Measuring the bath spectrum S(w) F(w, t) W w Continuous Rabi pulse The decay rate is G. Gordon et. al. , J. Phys. B: At. Mol. Opt. Phys. 42, 223001

Measured collisional bath spectrum Lorentzian Trap oscillation frequency I. Almog et. al. , submitted Measured collisional bath spectrum Lorentzian Trap oscillation frequency I. Almog et. al. , submitted (2011)

Measured decay vs predictions from bath spectrum I. Almog et. al. , submitted (2011) Measured decay vs predictions from bath spectrum I. Almog et. al. , submitted (2011)

Anomalous diffusion of atoms in a 1 D dissipative lattice Anomalous diffusion of atoms in a 1 D dissipative lattice

Motional broadening in real space Q=1. 0 Q=1. 57 Motional broadening in real space Q=1. 0 Q=1. 57

Measurements of 1 D anomalous diffusion Ballistic Diffusion Measurements of 1 D anomalous diffusion Ballistic Diffusion

Self similarity Self similarity

Summary Collisional narrowing PRL 105 093001 (2010) Discrete fluctuations PRL 104, 253003 (2010) Dynamical Summary Collisional narrowing PRL 105 093001 (2010) Discrete fluctuations PRL 104, 253003 (2010) Dynamical decoupling PRL 105 053201 (2010) Collisional broadening Bath characterization Anomalous diffusion PRA, in press (2011) submitted (2011) in preparation (2011)

Outline • Collisional narrowing Y. Sagi, I. Almog and ND, PRL 105 093001 (2010) Outline • Collisional narrowing Y. Sagi, I. Almog and ND, PRL 105 093001 (2010) • Spectrum with discrete fluctuations Y. Sagi, I. Almog, R. Pugatch and ND, PRL 104, 253003 (2010) • Motional broadening Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and ND, submitted (2010) • Dynamical decoupling Y. Sagi, I. Almog and ND, PRL 105 053201 (2010) • Bath spectral charecterization I. Almog et. al. , submitted (2011)

How to create a Power-law velocity distribution? • Don’t be in thermal equilibrium! • How to create a Power-law velocity distribution? • Don’t be in thermal equilibrium! • Sisyphus cooling scheme: Y. Castin, J. Dalibrad, C. Cohen-Tannoudji (1990)

Measurements of 1 D anomalous diffusion Ballistic Diffusion Measurements of 1 D anomalous diffusion Ballistic Diffusion

Measurements of 1 D anomalous diffusion It is possible to measure both the spatial Measurements of 1 D anomalous diffusion It is possible to measure both the spatial atomic distribution and the velocity distribution (by a time of flight method).

Direct observation of anomalous diffusion Direct observation of anomalous diffusion

1 D anomalous diffusion Ballistic Normal diffusion 1 D anomalous diffusion Ballistic Normal diffusion

Self similarity in the experiment Self similarity in the experiment

Self similarity in the experiment (2) Self similarity in the experiment (2)

Effect of cutoff Motional broadening persists until cutoff is sampled Effect of cutoff Motional broadening persists until cutoff is sampled

Optimal DD sequence for a Lorentzian bath G. S. Uhrig, Phys. Rev. Lett. 98, Optimal DD sequence for a Lorentzian bath G. S. Uhrig, Phys. Rev. Lett. 98, 100504 (2007).

Process tomography of non-linear Hamiltonian Process tomography of non-linear Hamiltonian

Mott insulator suppresses collisions • Mott-Insulator atom per site with exactly one • ~80 Mott insulator suppresses collisions • Mott-Insulator atom per site with exactly one • ~80 Hz EIT lines • ~250 msec storage time for light U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, PRL 2010

Measured collisional bath spectrum Lorentzian part Axial oscillation frequency Radial oscillation frequency Measured collisional bath spectrum Lorentzian part Axial oscillation frequency Radial oscillation frequency

Gaussian theory: Kubo’s model • An ensemble of oscillators with a distribution of resonant Gaussian theory: Kubo’s model • An ensemble of oscillators with a distribution of resonant frequencies. • If is a Gaussian process, the dephasing is given in terms of the correlation function by: • For a Poissonian fluctuations, we obtain:

The solution of the model Without collisions: With collisions: Where the tilde stands for The solution of the model Without collisions: With collisions: Where the tilde stands for the Laplace transform. The spectrum can be calculated by:

Measuring the bath spectrum Measuring the bath spectrum

B B

Dephasing of optically trapped atoms In our experiment For Gaussian phase distribution Dephasing of optically trapped atoms In our experiment For Gaussian phase distribution