![Page 1: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/1.jpg)
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
![Page 2: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/2.jpg)
in collaboration with:in collaboration with:in collaboration with:in collaboration with:
Mikhail Lukin (Harvard)Eugene Polzik (Kopenhagen)Anders Sørensen (Kopenhagen)
QUACS
![Page 3: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/3.jpg)
quantum networksquantum networksquantum networksquantum networks
|>
photons as information carrier atoms for storage and processing
![Page 4: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/4.jpg)
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
![Page 5: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/5.jpg)
outline:outline:outline:outline:
• perfect single-mode quantum memory
• Faraday scheme
• off-resonant Raman scheme
• EIT scheme
![Page 6: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/6.jpg)
outline:outline:outline:outline:
• perfect single-mode quantum memory
• Faraday scheme
• off-resonant Raman scheme
• EIT scheme
![Page 7: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/7.jpg)
outline:outline:outline:outline:
• perfect single-mode quantum memory
• Faraday scheme
• off-resonant Raman scheme
• EIT scheme
![Page 8: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/8.jpg)
outline:outline:outline:outline:
• perfect single-mode quantum memory
• Faraday scheme
• off-resonant Raman scheme
• EIT scheme
![Page 9: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/9.jpg)
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
![Page 10: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/10.jpg)
• bi-linear Hamiltonian:
assume:
![Page 11: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/11.jpg)
• solution of Heisenberg equation:
if determinant is nonzero (=1):
![Page 12: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/12.jpg)
• generic Hamiltonians for ideal mapping
(T) = / 2
![Page 13: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/13.jpg)
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
![Page 14: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/14.jpg)
• Stokes parameters of polarization state of light
• Spins of atomic ensemble
„macroscopic“ Hamiltonian
constant of motion
![Page 15: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/15.jpg)
• x – pol. coherent input light • initial atomic polarization
„macroscopic“ Hamiltonian
< S > = || / 2x2
non-ideal Hamiltonian mapping
![Page 16: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/16.jpg)
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
![Page 17: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/17.jpg)
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)
![Page 18: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/18.jpg)
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
![Page 19: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/19.jpg)
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
![Page 20: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/20.jpg)
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
![Page 21: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/21.jpg)
„stopping“ of light:
![Page 22: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/22.jpg)
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
![Page 23: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/23.jpg)
dark & bright-state polaritons:
in adiabatic limit:
![Page 24: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/24.jpg)
collective spin
light-stopping = adiabatic rotation of DSP: E spin
![Page 25: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/25.jpg)
polariton excitations:
|n |S = -N/2 |0 |S = -N/2 + n
= 0 = /2
polariton rotation:
=
ph ph at
at
![Page 26: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/26.jpg)
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:
![Page 27: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/27.jpg)
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
![Page 28: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/28.jpg)
choose
perfect mapping Hamiltonian
• drive-field + polarized• atoms z- polarized
![Page 29: Continuos-variable and EIT-based quantum memories: a common perspective Michael Fleischhauer Zoltan Kurucz Technische Universität Kaiserslautern DEICS](https://reader036.vdocuments.site/reader036/viewer/2022062714/56649d425503460f94a1d350/html5/thumbnails/29.jpg)
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