Ramsey Interference in One dimensional systems

Probing many-body systems of ultracold atoms Eugene Demler Harvard University T. Kitagawa (Harvard), S. Pielawa (Harvard), D. Pekker (Harvard), R. Sensarma (Harvard/JQI), V. Gritsev (Fribourg), M. Lukin (Harvard), Lode Pollet (Harvard)

Collaboration with experimental groups of T. Esslinger, I. Bloch, J. Schmiedmayer Harvard-MIT $$ NSF, MURI, DARPA, AFOSR Outline Lattice modulation experiments with fermions

Also yesterdays talks by Henning Moritz and Andreas Ruegg Ramsey interference experiments in 1d Lattice modulation experiments with fermions in optical lattice. Probing the Mott state of fermions Expts:

Theory: Joerdens et al., Nature (2008) Greif, Tarruell, Strohmaier, Moritz, Esslinger et al. Kollath et al., PRA (2006) Huber, Ruegg, PRA (2009) Sensarma et al. PRL 2009 Pollet, Pekker, Demler, unpublished Yesterdays talks by Henning Moritz and Andreas Ruegg

Lattice modulation experiments Probing dynamics of the Hubbard model Modulate lattice potential Measure number of doubly occupied sites Main effect of shaking: modulation of tunneling

Doubly occupied sites created when frequency matches Hubbard U Lattice modulation experiments Probing dynamics of the Hubbard model R. Joerdens et al., Nature 455:204 (2008) Mott state Regime of strong interactions U>>t.

Mott gap for the charge forms at Antiferromagnetic ordering at High temperature regime All spin configurations are equally likely. Can neglect spin dynamics. Doublon production rate depends on propagation of doublons and holes

Retraceable Path Approximation Brinkmann & Rice, 1970 preliminary data Spectral Fn. of single hole Doublon Production Rate Experimental data courtesy of D. Greif

Lattice modulation experiments. Sum rule Ad(h) is the spectral function of a single doublon (holon) Sum Rule : preliminary data courtesy of D. Greif

T-independent ? Simple model to include temperature dependence and trap: multiply production rate by the average fraction of nearest neighbors with opposite spins Ramsey Interference in one

dimensional systems Using quantum noise to study many-body dynamics One dimensional systems in condensed matter Non-perturbative effects of interactions: Absense of long range order Electron fractionalization 1d organics

carbon nanotubes GaAs/AlGaAs Heterostructures Emphasis on equilibrium properties and linear response 1d systems of ultracold atoms: analysis of nonequilibrium dynamics

Time evolution of coherence in split condensates S. Hofferberth et al., Nature (2007) 1D Ramsey Interferometry (Widera, et.al PRL 2008) Introduction: Ramsey Interference Ramsey interference

1 0 Atomic clocks and Ramsey interference: Working with N atoms improves the precision by . t

Ramsey Interference with BEC Single mode approximation Gaussian distribution of Sz Spin squeezing: possible application in quantum enhanced metrology Sorensen, Moller, Cirac, Zoller, Lewensstein,

Ramsey Interference with 1d 1d systems in optical lattices Ramsey interference in 1d tubes: A.Widera et al., B. PRL 100:140401 (2008) BEC

1d systems in microchips Two component BEC in microchip Treutlein et.al, PRL 2004 Ramsey Interference in 1d: a probe of many-body dynamics Ramsey interference in 1d condensates

Spin echo experiments A. Widera, et al, PRL 2008 Expect full revival of fringes Only partial revival after spin echo! Spin echo experiments in 1d tubes

Single mode approximation does not apply. Need to analyze the full model Low energy effective Hamiltonian for spin dynamics Bosonization Tomonaga-Luttinger Hamiltonian 1

Ramsey interference: Initial State After /2 pulse, spins point in x direction Small uncertainty in Initial state: squeezed state in s Wk determined from Short distance cut-off at spin healing length

related argument in Bistrizer, Altman, PNAS (2008) Ramsey interference in 1d Time evolution Luttinger liquid provides good agreement with experiments. A. Widera et al., PRL 2008. Theory: V. Gritsev Technical noise could also lead to the absence of echo Need smoking gun signatures

of many-body decoherece Distribution functions of Ramsey amplitude Distribution Probing spin dynamics through distribution functions Distribution function contains

information about higher order correlations Joint distribution function can also be obtained Interference of independent 1d condensates S. Hofferberth, I. Lesanovsky, T. Schumm, J. Schmiedmayer, A. Imambekov, V. Gritsev, E. Demler, Nature Physics (2008) Higher order correlation functions

probed by noise in interference Joint distribution functions Short segments |S|^2 does not change but Sx decays Long segments both Sx and |S|^2 decay

Two regimes of spin dynamics Modes with >l leads to the decay l leads to the decay of Sx but not |S| Modes with

Suggested unique signatures of the multimode decoherence of Ramsey fringes in 1d Ramsey interferometer combined with study of distribution function is a useful tool to probe many-body dynamics Joint distribution functions provide simple visualization of complicated many-body dynamics

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