prospect of using single photons propagating through rydberg eit medium for quantum computation

IOP, Bhubaneswar22nd Feb 2014

Prospect of using single photons propagating through Rydberg EIT medium for quantum computation

Ashok Mohapatra

National Institute of Science Education

and Research, Bhubaneswar

Outline

Introduction to quantum computation using photons

Introduction to Rydberg EIT and its non-linearity

Our experimental progress at NISER

Conclusion

Classical computer Quantum computer

Bit Qubit

0 or 1Polarization states: |H> or |V> |> = 1 |H> + 2 |V>

0 V or 5 V of atransistor output

2-level quantum system(e.g. Single photon)

Classical gatesAND, OR, NOT etc(Universal)

Single qubit rotation operatorsand 2-qubit Controlled-NOT gate(Universal quantum gates)

|α1|2+|α2|2=1

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 plateHadamard gate

Half wave platetwo Hadamard operation

CNOT gate:Interaction of photons

Kerr non-linearityof a medium

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.

Innn 20 )3(2 nwhere

n2 ≈ 10-20 m2/W for typical glass

Electromagnetically induced transparency (EIT)

Probe (Ωp)

F=2F=1

87Rubidium

5S1/2

5P3/2 F‘=3

nS1/2

6 MHz

Electromagnetically induced transparency (EIT)

87Rubidium

6 MHz

500 kHz

Probe (Ωp)

F=2F=1

5S1/2

5P3/2 F‘=3

nS1/2

σ +

σ -Coupling (Ωc)

EIT still doesn‘t provide enough non-linearity at single photon level

Rydberg EIT

Rydberg EIT:Mohapatra et al., PRL, 98, 113003 (2007) (Thermal atoms)Weatherill et al., J. Phys. B, 41, 201002 (2008) (Cold atoms)

87Rubidium

6 MHz

500 kHz

Probe (Ωp)

F=2F=1

5S1/2

5P3/2 F‘=3

nS1/2

σ +

σ -Coupling (Ωc)

Rydberg state

Rydberg atoms

Size n2

Dipole moment n2

Lifetime n3

Polarizability n7

van der Waals n11

Sensitivity to electric fields

Scaling with principal quantum number n (low)

Long lived100 μsec for n > 40

Strongly interacting(QIP)Atom - atom interactions

Rydberg states: large n

Strong dipolar interaction

Giant Kerr effect

5S1/2

5P3/2 5P1/2

Few 100 nm

Rydberg Rydberg interaction

66)(r

CrV

11n

Simplest case: van der Waals

Atomic distance

E

g,r

r,r

g,g

Ω

Rydberg blockade

66)(r

CrV

11n

Simplest case: van der Waals

blockade condition

66»

block

C

a

blocka few µmAtomic distance

E

g,r

r,r

g,g

Ω

blocka

Rydberg blockade

grerg i ,,2

1

≡Ω

2eff 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)

g

r

g

r

1 21

1... ...

N

i Ni

W g g r gN

eff N

Vogt et al., PRL 97, 083003 (2006)Heidemann et al., PRL 99, 163601 (2007)Raitzsch et al., PRL 100, 013002 (2008)

Superatom

Non-linearity of Rydberg EIT

6 MHz

500 kHz

Probe (Ωp)

F=1

Coupling (Ωc)

Rydberg stater

e

g

rgDcp

p

cp

c

2222

Dark state that doesn‘t couple to the probe beam and hence probe beam become transparent

Non-linearity of Rydberg EIT

ekrgDcp

p

cp

c

2222

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.

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 groupPritchard et al. PRL, 105, 193603 (2010)

Non-linearity of Rydberg EIT(Pushing to single photon level)

MIT groupPeyronel 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 EITin thermal vapor

• Rydberg blockade radius is only scaled approximately by a factor of 3 in 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

Dblock

Ca

66

Measurement of the non-linear refractive index Rydberg EIT medium

ω

ω+δ

Measurement of the non-linear refractive index Rydberg EIT medium

5s5s1/21/2(F=3)→5p(F=3)→5p3/23/2(F’)→45d(F’)→45d

5s5s1/21/2(F=3)→5p(F=3)→5p3/23/2(F’)→44s(F’)→44s

5s5s1/21/2(F=3)→5p(F=3)→5p3/23/2(F’)→49d(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

44d EIT spectra

Reference: Mohapatra et al. PRL (2007)

High precession spectroscopy (d - state fine structure splitting)

Mohapatra et al. PRL 98, 113003 (2007).K. C. Harvey et al, Phys. Rev. Lett. 38, 537 (1977).

W. Li, I. Mourachko, M. W. Noel, and T. F. Gallagher, Phys. Rev. A 67, 052502

(2003).

5s

5p

ns

Giant Kerr effect of Rydberg EIT mediumElectric field sensitivity of Rydberg state combined with the

non-linear properties of EIT

Giant Kerr effect of Rydberg EIT medium

5s

5p

ns ΔW

∆W:

1. Stark shift by applying an external Electric field (DC Kerr effect)

2. Interaction induced shift (Similar to AC Kerr effect)

20 0 0rn B E (DC Kerr effect)

Electric field sensitivity of Rydberg state combined with the non-linear properties of EIT

Experimental demonstration by phase modulation of light

AOM

+

-

Fast photodetector (1.2 GHz bandwidth)

Spectrum analyzer

Phase modulation of light (Sideband spectra)

N-dependence of the Kerr constant

α scales as n*7

Ωc scales as n*-3/2

c1 determines the absolute maximum

c2 determines the n* dependent scaling

20 0 0rn B E

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

AOM

Spectrum analyzer

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 rf-dressed 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)

Prof. C. S. AdamsDr. K. J. WeatherillMr. M. G. BasonMr. J. PritchardMr. R. Abel

Durham University Group

Frequency stabilization of blue laser to a EIT peak using frequency modulation scheme (schematic)

TopticaSHG

@ 480 nm

LP filter

Toptica FALC module Fast feedback to master current (BW ~ 1 MHz)

Slow feedback to master piezo

PIDStabilized to Polarization spectroscopy

EC

DL

@ 7

80 n

m

λ/2 λ/2

λ/4 λ/4EOM

Phase shifter

30 dBm power amplifier

20 dBamplifier

Photodetector1 MV/W, 10 MHz

Di-chroic mirror

Mixer

Top

tica

DL

pro

Home made EOM

D. J. McCarron et al., Meas. Sci. Tech. 2008

Ultra-stable, no long term drift and 100 kHz of relative line-width 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

Frequency stabilization of blue laser to a EIT peak using frequency modulation scheme

Kerr effect in Rydberg EIT medium


In the re

gime


Kerr effect (1875)

In the re

gime

Measurement of the Kerr effect of Rydberg EIT medium

5p - 32s

Jamin Interferometer


+ V

- V 5p - 32s

Jamin Interferometer

Both the lasers are locked to the EIT signalAbel et al., submitted to Appl. Phys. Lett.

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’)


For an ac electric field (E0) and dc field (E’) 2nd harmonic sidebands


Application toprecesion electrometry

Interaction of photons using EIT

F=1

nS1/2

1

2

3

Signalphoton 1

Coupling

Interaction of photons using EIT

F=1

nS1/2

Large 3rd order non-linearity with less absorption

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))

2

3

4

1

Signalphoton 1

Photon 2

Coupling

prospect of using single photons propagating through rydberg eit medium for quantum computation

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