Continuos-variable and EIT-Continuos-variable and EIT-based quantum memories: based quantum memories:

a common perspectivea common perspective

Michael FleischhauerMichael Fleischhauer

Zoltan KuruczZoltan Kurucz

Technische Universität KaiserslauternTechnische Universität Kaiserslautern

DEICS III / QUDAL Feb. 2006, Eilat, Israel

in collaboration with:in collaboration with:in collaboration with:in collaboration with:

Mikhail Lukin (Harvard)Eugene Polzik (Kopenhagen)Anders Sørensen (Kopenhagen)

QUACS

quantum networksquantum networksquantum networksquantum networks

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photons as information carrier atoms for storage and processing

atom-light interfaces:atom-light interfaces:atom-light interfaces:atom-light interfaces:

EIT scheme

(t)

(t)

probe

Fleischhauer, Lukin, PRL 2000; PRA 2002Phillips et al. PRL 2001, Kuzmich et al. Nature 2005Eisaman et al. Nature 2005

quasi-particle picture

?

Faraday scheme

probe

Julsgaard, Sherson, Cirac, Fiurášek, Polzik, Nature 2004Sørenson, Mølmer, … quant-ph/0505170, …

continuous variable picture

outline:outline:outline:outline:

• perfect single-mode quantum memory

• Faraday scheme

• off-resonant Raman scheme

• EIT scheme

outline:outline:outline:outline:

• perfect single-mode quantum memory

• Faraday scheme

• off-resonant Raman scheme

• EIT scheme

outline:outline:outline:outline:

• perfect single-mode quantum memory

• Faraday scheme

• off-resonant Raman scheme

• EIT scheme

outline:outline:outline:outline:

• perfect single-mode quantum memory

• Faraday scheme

• off-resonant Raman scheme

• EIT scheme

perfect single-mode memory:perfect single-mode memory: perfect single-mode memory:perfect single-mode memory:

light mode atomic ensemble

X P X PL L A A

• map of ideal q-memory:

M symplectic 2 x 2 matricesi

• bi-linear Hamiltonian:

assume:

• solution of Heisenberg equation:

if determinant is nonzero (=1):

• generic Hamiltonians for ideal mapping

(T) = / 2

Faraday rotation:Faraday rotation:Faraday rotation:Faraday rotation:

microscopic Hamiltonian

Julsgaard, Sherson, Cirac, Fiurášek, Polzik, Nature 2004Sørenson, Mølmer et al. quant-ph/0505170

• 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

xy

• 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

< S > = || / 2x2

non-ideal Hamiltonian mapping

single-pass Faraday scheme:single-pass Faraday scheme:single-pass Faraday scheme: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:fidelity of single-pass scheme:fidelity of single-pass scheme: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:double-pass Faraday scheme:double-pass Faraday scheme:double-pass Faraday scheme:

1. unitary evolution with H for t

• requires either atomic spin squeezing but no feedback

Sherson et al. quant-ph/0505170

1

2. unitary evolution with H for t´2

tt´= 1

• or perfect detection & feedback but no squeezing

triple-pass Faraday scheme:triple-pass Faraday scheme:triple-pass Faraday scheme:triple-pass Faraday scheme:

• ideal mapping w/o squeezing and feedback

operator identity

EIT scheme:EIT scheme:EIT scheme: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: quasi-particle picture of EIT: quasi-particle picture of EIT: 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 ph at

at

time-dependent :

perfect mapping Hamiltonian

effective Hamiltonian of dynamical EIT: effective Hamiltonian of dynamical EIT: effective Hamiltonian of dynamical EIT: effective Hamiltonian of dynamical EIT:

off-resonant Raman scheme:off-resonant Raman scheme:off-resonant Raman scheme:off-resonant Raman scheme:

• drive-field + polarized• atoms z- polarized

g / = g´ / ´ Faraday scheme S 2 2z z

choose

perfect mapping Hamiltonian

• drive-field + polarized• atoms z- polarized

summary:summary: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