Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS III / QUDAL Feb. 2006, Eilat, Israel

in collaboration with: Mikhail Lukin (Harvard) Eugene Polzik (Kopenhagen) Anders Sørensen (Kopenhagen) QUACS

quantum networks |>|> photons as information carrieratoms for storage and processing

atom-light interfaces: EIT scheme  (t) probe Fleischhauer, Lukin, PRL 2000; PRA 2002 Phillips et al. PRL 2001, Kuzmich et al. Nature 2005 Eisaman et al. Nature 2005 quasi-particle picture ? Faraday scheme  probe Julsgaard, Sherson, Cirac, Fiurášek, Polzik, Nature 2004 Sørenson, Mølmer, … quant-ph/ , … continuous variable picture

outline:outline: perfect single-mode quantum memory Faraday scheme off-resonant Raman scheme EIT scheme

outline:outline: perfect single-mode quantum memory Faraday scheme off-resonant Raman scheme EIT scheme

outline:outline: perfect single-mode quantum memory Faraday scheme off-resonant Raman scheme EIT scheme

outline:outline: perfect single-mode quantum memory Faraday scheme off-resonant Raman scheme EIT scheme

perfect single-mode memory: perfect single-mode memory: light modeatomic ensemble XP X P LL A A map of ideal q-memory: M symplectic 2 x 2 matrices i

bi-linear Hamiltonian: assume:

solution of Heisenberg equation: if determinant is nonzero (=1):

generic Hamiltonians for ideal mapping  (T) =  / 2

Faraday rotation: microscopic Hamiltonian Julsgaard, Sherson, Cirac, Fiurášek, Polzik, Nature 2004 Sørenson, Mølmer et al. quant-ph/ strong coherent field with linear polarization in x direction i.e. x =  + and  - atoms are spin polarized in x direction, i.e. (|1> + |2>)/  2 z x y

Stokes parameters of polarization state of light Spins of atomic ensemble „macroscopic“ Hamiltonian constant of motion

x – pol. coherent input light initial atomic polarization „macroscopic“ Hamiltonian = |  | / 2 x 2 non-ideal Hamiltonian mapping

single-pass Faraday scheme: unitary evolution for time t requires atomic spin squeezing requires perfect detection & feedbeack L measurement of light component X  x and momentum displacement –x/t of atoms (feedback) Julsgaard et.al, Nature 2004

Gaussian state fidelity of single-pass scheme: non-Gaussian states (  = 0) coherent spin and light state, pefect detector (  =0),  F ≤ 82 % coh. spin state (CSS)

double-pass Faraday scheme: 1. unitary evolution with H for t requires either atomic spin squeezing but no feedback Sherson et al. quant-ph/ unitary evolution with H for t´ 2 tt´= 1 or perfect detection & feedback but no squeezing

triple-pass Faraday scheme: ideal mapping w/o squeezing and feedback operator identity

EIT scheme:  Fleischhauer, Lukin, PRL 2000; PRA 2002; Phillips et al. PRL 2001, Kuzmich et al. Nature 2005; Eisaman et al. Nature 2005 dynamically controllable group velocity 2 3

„stopping“ of light:

Autler-Townes splitting   quasi-particle picture of EIT: large small

dark & bright-state polaritons: in adiabatic limit:

collective spin light-stopping = adiabatic rotation of DSP: E  spin

polariton excitations: |n  |S = -N/2  |0  |S = -N/2 + n   = 0  =  /2 polariton rotation: = ph at

time-dependent  : perfect mapping Hamiltonian effective Hamiltonian of dynamical EIT:

off-resonant Raman scheme: drive-field  + polarized atoms z- polarized g /  = g ´ /  ´  Faraday scheme S  22 zz

choose perfect mapping Hamiltonian drive-field  + polarized atoms z- polarized

summary:summary: perfect single-mode quantum memory single-pass Faraday scheme + squeezing and feedback double-pass Faraday scheme + squeezing or feedback triple-pass Farday scheme EIT scheme