Low-Light-Level Cross Phase Modulation with Cold Atoms

1
Low-Light-Level Cross Phase Modulation with Cold
Atoms

• J.H. Shieh, W.-J. Wang and Ying-Cheng Chen
• Institute of Atomic and Molecular Sciences,
  Academia Sinica, NTHU AMO Seminar, March 3, 2009

2
Outline

• Introduction to Cross Phase Modulation (XPM)
• Briefs on Electromagnetically induced
  transparency (EIT)
• Introductions on EIT-based XPM schemes
• Considerations on few-photon-level XPM
• Our experimental progress towards the goal
• Prospective

3
Cross Phase Modulation
Probe light
Control light
atoms
Photon can couple to photon via the media (e.g.
atoms).
Photon-photon has no coupling in free space, at
least at low field strength where QED effect is
not significant.
f
Without control light
With control light
Kerr effect nn0n2I
Cross phase modulation Phase change of the probe
pulse under the presence of control pulse and
media. The Kerr effect.

• One of the holey grail in nonlinear optics is to
  observe the p radian mutual phase shift for two
  single photon pulses with small absorption loss.

4
XPM Application Controlled-NOT gate for Quantum
Computation

• CNOT and single qubit gates can be used to
  implement an arbitrary unitary operation on n
  qubits and therefore are universal for quantum
  computation.
• Single photon XPM can be used to implement the
  quantum phase gate and CNOT gate

Truth table for CNOT gate
PBS
PBS
Signal
Control qubit
Atoms
Probe
Target qubit
For a good introductory article, see ?????? CPS
Physics Bimonthly, 524, Oct. 2008
5
XPM in Generation of Entangled Photon Pairs

• Single photon p phase shift XPM can be
  implemented to generate entangled photon pairs
  which are important in quantum teleportation.
• For a close look at quantum teleportation, see
  e.g. 2008 AMO summer school presentation file in
  NCTS website given by ???.

PBS
PBS
Signal
450 linear polarization
Entangled photon pairs
Atoms
Probe
6
XPM in Quantum Nondemolition Measurement
Signal beam
Meter beam

• QND measurement of the photon number by
  dispersive atom field coupling. See. e.g. Scully,
  Quantum Optics, Sec.19-3.

7
Electromagnetically Induced Transparency
(EIT),the Phenomena
3gt
Attenuated
Atomic sample
Attenuated
Probe laser
1gt
Optical density2
Transparent!
3gt
Pass through again
Probe laser
Coupling laser
2gt
1gt
For a review, see Rev. Mod. Phys. 77, 633,2005
8
EIT, the Physical Explanation

• Destructive interference between excitation
  pathways
• Destructive interference between two dressed
  states
• Dark state or resonance

3gt
coupling
probe




2gt
1gt
Path ii
Path i
Path iii
3gt
coupling
probe
2gt
probe
3gt
1gt
A limiting case of coherent population trapping
effect where
Diagonalize the HAHACHAP
coupling
probe
9
EIT and the Slow Light

• Group velocity of the probe pulse
• The steep dispersion in addition with no loss has
  important effect on the probe propagation in EIT
  medium the lossless slow light.

Vglt17m/s, Hau et.al. Nature397,594,1999
10
More on Slow Light

• If ?/G3ltlt1 dc0,
• Higher order dispersion and finite EIT bandwidth
  still cause slightly pulse spreading.
• At dp0, one obtains (N atom density)
• Group delay for a sample with length L
• The slow light has practical applications as
  optical delay line.

considering the decoherence
11
Line Narrowing Effect with Large OD Gas

• Has been observed in warm gas, PRL 79,2959,1997.
• Intensity transmission
• For medium and large OD,
• Delay Bandwidth product

12
Slow Light Dark-State Polariton
3gt
3gt
3gt
coupling
coupling
coupling
probe
probe
2gt
2gt
2gt
1gt
1gt
1gt
Light component
Matter component atomic spin coherence
LukinFleischhauer, PRL 84,5094,2000
13
EIT and the Photon Storage

• By adiabatically turn off the coupling light, the
  probe pulse can completely transfer to atomic
  spin coherence and stored in the medium and can
  be retrieved back to light pulse later on when
  adiabatically turn on the coupling.
• This effect can be used as a quantum memory for
  photons.
• The photon storage and retrieved process has been
  proved to be a phase coherent process by Yus
  team.

coupling
probe
Hau et.al. Nature, 409,490,2001
Y.F. Chen et.al. PRA 72, 033812, 2005
14
Basic EIT-based XPM scheme N-type system
With signal beam
Without signal
probe
signal
coupling

• The scheme was proposed by Schmidt Imamoglu
  (Opt. Lett. 21,1936,1996).
• The signal beam cause ac Stark shift on state 2
  and introduce a cross phase
• modulation on probe.
• The EIT guarantee low probe loss with the
  transparency window if choosing
• larger enough coupling field.
• The scheme was firstly demonstrated by Yi-Fu
  Zhus team (PRL91,093601,2003).

15
Dual Slow Light Scheme for Weak Field XPM
Lukin Imamoglu PRL 84,1419,2000
Both signal and probe are slow-light pulses

• Use a second species atom and a second coupling
  pulse to allow signal pulse becoming a slow light
  pulse.
• Both signal and probe pulses are tuned to the
  same slow group velocity. This allow long
  interaction time between these two weak pulses to
  gain significant mutual phase shift.
• Long delay time -gt high OD
• Avoid loss due to absorption by decreasing the
  decoherence rate

Tightly focusing
Long interaction time
16
Single Species Dual Slow Light Weak Field XPM

• The symmetric arrangement guarantee the matched
  group velocity for the two weak probe pulses for
  long interaction length.
• Each probe pulse is the signal pulse of the
  N-type system for the other EIT system.
• The Zeeman shift gtgt Natural linewidth for
  dispersive coupling in the N-type system.
• Two coupling fields are needed.
• The orthogonal coupling and probe requires very
  cold sample to minimize the residual Doppler
  broadening.
• The two probe pulses can be used to implement the
  quantum phase gate with the qubit as polarization
  states.

probe
signal
PRA 65,033833,2002
17
N-Tripod Scheme XPM

• Both signal and probe form EIT with single
  coupling beam and can be tuned with coupling
  intensity and detuning and population difference
  to match the group velocity.
• Both signal and probe can be on exact EIT
  resonance but still experience XPM.
• Signal beam cause a cross phase modulation on
  probe but also a self phase modulation.
• Utilize Zeeman shift such that signal beam is
  mainly dispersive coupling in the N-type system
• Similar to previous scheme, one can implement the
  quantum phase gate with polarization state as
  qubits..

m1
m3
6P3/2,F3
m0
6S1/2,F4
m2
6S1/2,F3
m0
Cs
PRL 97,063901,2006 Opt. Comm. 681,2040,2008
18
N-Tripod
Probe
Signal
Im(?)
Linear susceptibility
Re(?)
Nonlinear susceptibility
19
The Light-Storage XPM Scheme

• Proposed and demonstrated by Yus team, PRL
  96,043603,2006.
• Convert and store probe light into atomic spin
  coherence. Signal beam is applied during the
  storage time to interact with atom.
• A phase shift of 440 for probe pulse was
  obtained with a 2-µs signal pulse of Rabi
  frequency 0.32G with 65 transmission.
• The energy per unit area of signal beam,
  O2t,affect the phase shift at a fixed detuning.
• To increase the phase shift, one has to tightly
  focus the probe and signal beam to increase the
  interaction strength and also to increase the
  interaction time of signal with atoms.

coupling
Phase shift
probe
Probe attenuation e-a
t
signal
20
Few-Photon-Level XPM

• Large Kerr Nonlinearity
• Low loss
• Strong focusing to increase the atom-laser
  interaction strength
• Long atom-laser interaction time
• Possible schemes
• Using the high-finesse cavity
• Couple atoms and Light into the hollow core fiber
• Using the EIT-based stationary light scheme
  together with transverse waveguiding effect
• All are challenging !

High-finesse cavity
cold atom
Coupling probe
Signal beam
21
Experimental Progress Dense atomic medium

• In all EIT-based applications, the large optical
  density together with small decoherence rate are
  crucial requirements.
• We have obtained optical density gt 100 using
  2-dimensional MOT.
• To obtain atomic sample with even larger OD, the
  optical dipole trapping is required and is
  underway.

7cm
Absorption Spectrum
Optical density105
Optics Express. Chen Yu 16,3754(2008)
22
Small Decoherence Rate

• To obtain small decoherence rate, good mutual
  coherence between coupling and probe lasers and
  small inhomogeneity in magnetic field are
  crucial.
• We obtained phase locking via the modulation with
  vertical-cavity surface-emitting laser (VCSEL)
  and injection locking.
• Obtained phase locking between coupling and VCSEL
  with 13dBm modulation power at 9 GHz with
  sideband power ratio 15.
• Checked with beatnote by spectrum analyzer
  showing that the linewidth between coupling and
  probe to be lt 10Hz, the instrument resolution
  limit.
• Has been applied in the EIT experiments.

Coupling ECDL
RF
Bias-Tee
Idc
VCSEL
PBS
?/2
Probe DL
coupling
9GHz
VCSEL
frequency
Probe
23
Compensation of Stray Magnetic Field

• Three pairs of compensation coils with relative
  large size (50 cmf) are used with 6 independent
  current channels applied to null the stray field
  and gradients.
• Stary field is minimized to lt 30mG level by the
  linewidth of EIT spectrum.
• Non-metal support for MOT magnetic coils is used
  to avoid the induced eddy current when the MOT
  coils are turned off.
• Current through MOT coils is rapidly turned off
  (30 µs) by field-effect-transitors together with
  large damping resistor in parallel with coils.
• Two layers of mu-metal are used to shield the ion
  pump nearby the MOT.
• Even with all of these, we observed that the MOT
  inhomogeneous magnetic field decay completely
  after 2 ms possibly due to the induction of
  nearby metal stuffs.
• We are using Faraday rotation effect to allow a
  fast and quantitative diagnosis of stray field
  situations.

3GHz away from resonance
PRA, 59,4836,1999
24
Typical EIT Spectrum

• Obtained EIT with 50 transmission at 200kHz
  FWHM for OD70 with coupling intensity 5 mW/cm2.

25
Line Narrowing Effect with Large OD Gas

• Has been observed in warm gas, PRL 79,2959,1997.
• Intensity transmission
• For medium and large OD,

Increasing the OD of atom cloud
26
The Slow Light

• The typical delay time is 5-10 µs.
• Delay time gt 10µs is observed at the expense of
  higher loss.

27
The Light Storage

• Observed the light storage signal. However, the
  storage time is still short. Better compensation
  on the stray magnetic field is underway to
  decrease the decoherence rate further.

28
Prespectives

• Short term
• Study the oscillatory effect of transverse
  magnetic field on slow light.
• Realize the N-Tripod XPM in the two-dimensional
  MOT
• Middle term
• Obtain even higher OD gas in the optical dipole
  trap.
• Study the transverse waveguiding effect and XPM
  enhancement
• Long term
• Use the optical cavity with the light-storage XPM
  scheme to reach the few-photon-level XPM.

29
Oscillatory Behavior on Slow Light with
Transverse Magnetic Field

• Why the oscillating behavior in transverse
  magnetic field?
• What does the period corresponding to?
• Does this behavior exist in Cs?
• If yes, what is the value of the period?
• Preliminary experiment on Cs do suggest similar
  transverse magnetic field effect on delay time.
  Better calibration on compensation coils using
  Faraday rotation is underway.

87Rb, Yus team
30
N-Tripod XPM Scheme

• Optical pumping and/or microwave transitions to
  prepare the population.
• Magnetic field 30 Gauss to allow dispersive
  coupling for N-type system (?4G)
• Beatnote interferometer proposed by Yus team
  will be utilized to see the XPM phase shift.
• The experiment should be quite straightforward!

m1
m3
6P3/2,F3
m0
6S1/2,F4
m2
6S1/2,F3
m0
Cs
PRA 72,033812,2005