Prospect of using single photons
propagating through Rydberg EIT medium
for quantum computation
Ashok Mohapatra
National Institute of Science Education
and Research, Bhubaneswar
IOP, Bhubaneswar
22nd Feb 2014
Outline
 Introduction to quantum computation using
photons
 Introduction to Rydberg EIT and its nonlinearity
 Our experimental progress at NISER
 Conclusion
Classical computer
Bit
Quantum computer
Qubit
0 V or 5 V of a
transistor output
2-level quantum system
(e.g. Single photon)
0 or 1
Polarization states: |H> or |V>
|> = 1 |H> + 2 |V>
|α1|2+|α2|2=1
Classical gates
AND, OR, NOT etc
(Universal)
Single qubit rotation operators
and 2-qubit Controlled-NOT gate
(Universal quantum gates)
Qunatum computation using
photons
•
•
•
•
Single photon source
Single photon detctors
Optical elements for gate operation
A Kerr non-linear medium for interactions of
photons to devise a CNOT gate
Single qubit quantum gates
• Each photon as a qubit with two orthogonal polarized
state
Quarter wave plate
Hadamard gate
Half wave plate
two Hadamard operation
CNOT gate:
Interaction of photons
Kerr non-linearity
of a medium
n  n0  n2 I
where
n2   (3)
n2 ≈ 10-20 m2/W for typical glass
Increasing the length doesn‘t help due to strong
absorption in the medium
Electromagnetically Induced Transparency (EIT)
provides a larger 3rd order non-linearity without
absorption.
Electromagnetically induced
transparency (EIT)
nS1/2
6 MHz
5P3/2 F‘=3
Probe (Ωp)
5S1/2
F=2
F=1
87Rubidium
Electromagnetically induced
transparency (EIT)
nS1/2
Coupling (Ωc)
σ6 MHz
5P3/2 F‘=3
500 kHz
Probe (Ωp)
5S1/2
σ+
F=2
F=1
87Rubidium
EIT still doesn‘t provide enough non-linearity at single photon level
Rydberg EIT
Rydberg state
nS1/2
Coupling (Ωc)
σ6 MHz
5P3/2 F‘=3
500 kHz
Probe (Ωp)
5S1/2
σ+
F=2
F=1
87Rubidium
Rydberg EIT:
Mohapatra et al., PRL, 98, 113003 (2007) (Thermal atoms)
Weatherill et al., J. Phys. B, 41, 201002 (2008) (Cold atoms)
Rydberg atoms
Rydberg states: large n
Scaling with principal quantum number n (low)
5P3/2
5P1/2
Size
n2
Few 100 nm
Dipole moment
n2
Strong dipolar
interaction
Lifetime
n3
Long lived
100 μsec for n > 40
Polarizability
n7
Giant Kerr effect
Sensitivity to electric fields
van der Waals
5S1/2
Atom - atom interactions
n11
Strongly interacting
(QIP)
Rydberg Rydberg interaction
Simplest case: van der Waals
n11
r,r
Ω
E
C6
V (r )  6
r
g,r
g,g
Atomic distance
Rydberg blockade
Simplest case: van der Waals
n11
r,r
Ω
E
C6
V (r )  6
r
blockade condition
g,r
g,g
ablock
Atomic distance
C6
» 
6
ablock
ablock 
few µm
Rydberg blockade
r
r
Ω
≡
g
g
 
Urban et al., Nature Phys. 5, 110 (2009)
Gaetan et al., Nature Phys. 5, 115 (2009)
Wilk et al., Phys. Rev. Lett. 104, 010502 (2010)

1
g , r  ei r , g
2
eff  2

1 

W 
  g1 g2 ...ri ...g N 
N  i 1

N
eff  N 
Superatom
Vogt et al., PRL 97, 083003 (2006)
Heidemann et al., PRL 99, 163601 (2007)
Raitzsch et al., PRL 100, 013002 (2008)
Non-linearity of Rydberg EIT
Rydberg state
r
Coupling (Ωc)
6 MHz
e
500 kHz
Probe (Ωp)
g
F=1
D 
c

2
p

2
c
g 
p
 
2
p
2
c
r
Dark state that doesn‘t couple to the probe
beam and hence probe beam become transparent
Non-linearity of Rydberg EIT
In the blockade sphere, more than one atom can not be excited which
makes the dark state very fragile and get mixed with intermediate state.
D 
c

2
p

2
c
g 
p
 
2
p
2
c
r k e
For large probe power, the EIT peak reduces with larger probe absorption.
(a) One, (b) two, (c) three atoms per
blockade sphere
Durham university, UK group
Pritchard et al. PRL, 105, 193603 (2010)
Non-linearity of Rydberg EIT
(Pushing to single photon level)
MIT group
Peyronel et al. Nature, 488, 57 (2012)
Non-linearity of Rydberg EIT
(Pushing to single photon level)
MIT group, 2013, Firstenberg et al.
www.nature.com/doifinder/10.1038/nature12512
Optical non-linearity of Rydberg EIT
in thermal vapor
• Rydberg blockade radius is only scaled
C6
6
ablock 
approximately by a factor of 3 in
 D
thermal vapor
– Kuebler et al. Nature Photo. 4, 112 (2010)
• Optical pumping rate to the dark state is much faster than the
transit time of the atoms
Measurement of the non-linear
refractive index Rydberg EIT medium
ω
ω+δ
Measurement of the non-linear
refractive index Rydberg EIT medium
ω
ω+δ
Measurement of the non-linear
refractive index Rydberg EIT medium
5s1/2(F=3)→5p3/2(F’)→45d
5s1/2(F=3)→5p3/2(F’)→44s
5s1/2(F=3)→5p3/2(F’)→49d
Acknoledgement
Arup Bhowmik (PhD)
Sabyasachi Barik (Int. MSc)
Surya Narayan Sahoo (Int. MSc)
Charles Adams group at Durham University
Rydberg EIT with large probe power
EIT with large probe power
Rydberg EIT in thermal vapor
Rydberg EIT in thermal vapor
44d EIT spectra
Reference: Mohapatra et al. PRL (2007)
High precession spectroscopy
(d - state fine structure splitting)
K. C. Harvey et al, Phys. Rev. Lett. 38, 537 (1977).
Mohapatra et al. PRL 98, 113003 (2007).
W. Li, I. Mourachko, M. W. Noel, and T. F. Gallagher, Phys. Rev. A 67, 052502 (2003).
Giant Kerr effect of Rydberg EIT medium
Electric field sensitivity of Rydberg state combined with the
non-linear properties of EIT
ns
5p
5s
Giant Kerr effect of Rydberg EIT medium
Electric field sensitivity of Rydberg state combined with the
non-linear properties of EIT
ΔW
ns
5p
5s
∆W:
1. Stark shift by applying an
external Electric field (DC
Kerr effect)
2. Interaction induced shift
(Similar to AC Kerr effect)
nr  0 B0 E
2
(DC Kerr effect)
0
Experimental demonstration by phase
modulation of light
Spectrum
analyzer
Fast photodetector
(1.2 GHz bandwidth)
AOM
+
-
Phase modulation of light
(Sideband spectra)
Phase modulation of light
(Sideband spectra)
N-dependence of the Kerr constant
nr  0 B0 E
2
0
α scales as n*7
Ωc scales as n*-3/2
c1 determines the
absolute maximum
c2 determines the n*
dependent scaling
Kerr effect in Rydberg EIT medium
(Order of magnitude calculation)
•
•
•
•
•
Gas (CO2, 1 atm)
B0 ≈ 10-18 m/V2
Water
B0 ≈ 10-16 m/V2
Glass
B0 ≈ 10-14 m/V2
Nitrobenzene
B0 ≈ 10-12 m/V2
Rydber dark state
(thermal atoms)
B0 ≈ 10-6 m/V2
6 orders of magnitude bigger
• 10 orders of magnitude is expected for cold atoms
Noise spectra
Spectrum
analyzer
AOM
More on Electro-optic and electrometry
• Electro-optic control of Rydberg dark state
polariton
Bason et al. PRA 77, 032305 (2008)
• Enhanced electric field sensitivity of rfdressed Rydberg dark states (Bason et al.
Bason et al. New J. Phys. 12, 065015 (2010)
Outlook
• QIP using thermal atoms in microcell
– Quantum computation using photon
– Single photon source
– Quantum computation using mesoscopic ensemble
of atoms
• Versatile electric field sensor
• THz imaging
THz imaging
Replace the EO crystal by Rydberg EIT in a microcell filled with thermal atoms
(Preliminary idea)
Durham University Group
Prof. C. S. Adams
Dr. K. J. Weatherill
Mr. M. G. Bason
Mr. J. Pritchard
Mr. R. Abel
Frequency stabilization of blue laser to a EIT peak
using frequency modulation scheme (schematic)
EOM
λ/4
λ/4
Di-chroic mirror
λ/2
λ/2
30 dBm
power amplifier
Photodetector
1 MV/W, 10 MHz
20 dB
amplifier
Phase
shifter
ECDL
@ 780 nm
Toptica DL pro
Mixer
Toptica
SHG
@ 480 nm
Slow feedback to
master piezo
Stabilized to
Polarization
spectroscopy
LP filter
PID
Toptica FALC module
Fast feedback to master
current (BW ~ 1 MHz)
Home made EOM
D. J. McCarron et al., Meas. Sci. Tech. 2008
Frequency stabilization of blue laser to a EIT peak
using frequency modulation scheme
Ultra-stable, no long term drift
and 100 kHz of relative linewidth observed with 1 μW of
probe power
Stabilization demonstrated for
26D5/2 state by using less than
2 mW of blue light
For 58D3/2 state, less than
15 mW of blue light was used
Abel et al, under preparation
Kerr effect in Rydberg EIT medium
Kerr effect in Rydberg EIT medium
Kerr effect in Rydberg EIT medium
Kerr effect in Rydberg EIT medium
Kerr effect
(1875)
Measurement of the Kerr effect of
Rydberg EIT medium
5p - 32s
Jamin Interferometer
Measurement of the Kerr effect of
Rydberg EIT medium
+V
-V
5p - 32s
Jamin Interferometer
Both the lasers are locked to the EIT signal
Abel et al., submitted to Appl. Phys. Lett.
Measurement of the Kerr effect of
Rydberg EIT medium
N-dependence of the Kerr constant
Sidebands on Rydberg dark states
For small modulation frequency and
Stark shift compared to any dipole
allowed transition
Ω=-1/2αE2
Phase modulation of Rydberg dark states
Ω/2
2nd order sidebands
1st harmonic sidebands
For an ac electric field (E0) and dc field (E’)
1st harmonic sidebands
For an ac electric field (E0) and dc field (E’)
2nd harmonic sidebands
1st harmonic sidebands
Application to
precesion electrometry
Interaction of photons using EIT
3
nS1/2
Coupling
Signal
photon 1
2
1
F=1
Interaction of photons using EIT
4
3
nS1/2
Coupling
Signal
photon 1
Photon 2
2
1
Large 3rd order non-linearity with less absorption
F=1
But, still not enough to have π-phase shift to devise a
useful phase gate at single photon level
(Shapiro et al., PRA, 73, 062305 (2006))