cavity quantum computing with n-atom qubits · outline •vacuum-induced transparency (vit ) –...
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Photon-Photon Interactions
Massachusetts Institute of Technology MIT-Harvard Center for Ultracold Atoms
VIT, One-photon transistor Rydberg polaritons Wenlan Chen Thibault Peyronel Kristi Beck Ofer Firstenberg Michael Gullans Qi-Yu Liang Haruka Tanji-Suzuki Alexei Gorshkov Thomas Pohl Mikhail Lukin Vladan Vuletic
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Outline
• How to induce deterministic photon-photon interactions? For – All-optical switches (classical and quantum) – Photon-photon quantum gates – Quantum gas of interacting photons
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Outline • Vacuum-induced transparency (VIT)
– Induce transmission with an electromagnetic vacuum field;
• All-optical one-photon transistor – One photon controls one or many photons;
• Quantum nonlinear medium via Rydberg states – Optical medium that transmits one but absorbs two
photons; – Attracting photons.
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Goal: nonlinear optics with single-photons How can one make light interact influence the propagation of other light? Convert red photon into an atomic excitation, atom in other state can influence the propagation of blue photon, read out the red photon.
Two problems: i) one atom does not influence strongly the propagation of a light beam: σ/A < λ2/A < 1. ii) A single atom emits a red photon uniformly, not into incident mode.
A
atom
gate photon
source photon
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Goal: nonlinear optics with single-photons
• Mode-matching problem: Convert atomic excitation coherently back to light propagating in definite direction: array of phased dipoles – electromagnetically induced transparency (EIT)
Strong interaction problem: use cavity to multiply σ/A by number of photon round trips. or Use strongly interacting atomic states (Rydberg).
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Electromagnetically Induced Transparency
• EIT produces slow light by converting photons into collective atomic (spin) excitations
slow-light polariton 0 < v < c
=
Strength of control field determines probability amplitudes and speed of polariton: EIT linear in probe field
photon v=c
Probe photon
Control field
magnon v=0
Control field
+
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Vacuum-induced transparency
H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletic, Science 333, 1266 (2011).
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From EIT to VIT
• EIT is linear because control field is classical, i.e. nc≈nc+1
• If nc could be made small, then there would be strong nonlinearity:
• nc =0: vacuum-induced transparency, VIT
Probe photon
Control Field nc
Control Field nc+1
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Vacuum-induced transparency
• J. E. Field, Phys. Rev. A 47, 5064 (1993). Strongly coupled cavity can play role of control field.
• Nikoghosyan and Fleischhauer, PRL 104,
013601 (2010): nonlinearity can be used for dispersive photon Fock state filter
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Single-atom work on EIT with cavity
• Rempe group: M. Mucke, et al., Nature 465, 755 (2010).
• Meschede group: T. Kampschulte, et al., Phys. Rev. Lett. 105, 153603 (2010).
• Blatt group: L. Slodicka et al., Phys. Rev. Lett. 105, 153604 (2010).
• Above systems use cavity on probe leg to enhance the probe interaction with single atom
• Vacuum-induced transparency is different: cavity replaces control field, rather than enhancing probe field.
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Setup for observing VIT
133Cs
133Cs ensemble
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Large strongly coupled cavity
Cavity parameters: Length 1.4 cm Finesse 6×104
Waist 35 µm Cavity linewidth 2π 160 kHz Atomic linewidth 2π 5.2 MHz vacuum Rabi freq. 2π 1.3 MHz Cooperativity 8.1 Γ > g > κ
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Probe transmission and VIT
Probe transmission
Cavity emission
H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletic, Science 333, 1266 (2011).
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From VIT to EIT: nc>0 Tr
ansm
issi
on
Fill cavity with control photons
nc=10
nc=0 nc=0
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From VIT to EIT: transparency vs. cavity photon number
Cavity photon number
T
rans
pare
ncy
⟨nc⟩=0
⟨nc⟩=1
Strong nonlinearity: One cavity photon substantially changes probe transmission
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Dispersive photon Fock state filter
|α⟩ |1⟩ |2⟩ |3⟩
|1⟩ |2⟩ |3⟩
Nikoghosyan and Fleischhauer, PRL 104, 013601 (2010). Requires large cooperativity and large optical depth η ~ OD » 1
time
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Two photons incident on different parts of the ensemble interact via the cavity mode: Each photon influences the other’s group velocity, phase.
Probe photon
Control Field nc
Control Field nc+1
Infinite-range photon-photon interaction
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probe
Vacuum-induced transparency for two-level atoms?
Transparency as cavity field cancels incident field at atom: free space emission suppressed, dominant decay via cavity Alsing, Cardimona, and Carmichael, PRA 45, 1793 (1992). P. R. Rice, R. J. Brecha, Opt. Comm. 126, 230 (1996).
Detuning
Tran
smis
sion
Classical description: Tanji-Suzuki et al., Adv. At. Mol. Opt. Phys. 60, 201-237 (2011), quant-ph 1104.3594.
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One-photon optical switch and transistor Wenlan Chen Michael Gullans Kristin Beck Mikhail Lukin Haruka Tanji-Suzuki
Wenlan Chen, Kristin Beck, Michael Gullans, Mikhail Lukin, Haruka Tanji-Suzuki, and Vladan Vuletic, submitted (2013).
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EIT nonlinearity in four-level system
e.g., Imamoglu, Woods, Schmidt & Deutsch, PRL 79, 1467 (1997); S. Harris & Y. Yamamoto, PRL 81, 3611 (1998);
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Transistor with stored gate photon
control
gate recovery
signal
gate
gate storage
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Cavity transmission vs. gate photon number
⟨ng⟩ 1 2 3 0
⟨ng⟩=0
⟨ng⟩=0.8
⟨ng⟩=1.7
⟨ng⟩=2.8
Cavity detuning
tran
smis
sion
tran
smis
sion
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Histograms of cavity transmission ⟨ng⟩=0
⟨ng⟩=0
ng=0
ng=1
ng=0
ng=1
Clear separation of gate photon number states zero and one.
Det
ecte
d so
urce
pho
tons
experiment
theory
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Gain saturation at G~2000 presumably due to optical pumping to other sublevels with weaker coupling to cavity.
Single-photon transistor with gain: switching 1000 photons with one
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Gain saturation: optical pumping
nin=200 nin=330
nin=800 nin=2000
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Transistor with recovered gate photon
control
gate recovery
signal
gate
gate storage
Switched signal photon number
Gat
e ph
oton
reco
very
(arb
. u.)
Non-demolition gain: 2.3 signal photons can be switched while recovering gate photon with 1/e probability.
0
1
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Future possibilities • Quantum non-demolition detector
for traveling optical photons • N00N state preparation • Photon-photon quantum gates? • All-optical circuits with feedback
and gain in analogy to electronic circuits
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Single-photon nonlinearity by means of Rydberg polaritons Thibault Peyronel Qiyu Liang Ofer Firstenberg Alexey Gorshkov Thomas Pohl Mikhail Lukin
T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A.V. Gorshkov, T. Pohl, M.D. Lukin, and V. Vuletic, Nature 488, 57-60 (2012).
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Rydberg atoms for quantum control • Nonlinearities in Rydberg excitation
– Tong, D. et al. Local blockade of Rydberg excitation in an ultracold gas. PRL 93, 063001 (2004);
– Singer et al., PRL 93, 163001 (2004); – Liebisch et al., PRL 95, 253002 (2005); – Heidemann et al. , PRL 100, 033601 (2008).
• Quantum gate between two Rydberg atoms – Urban et al., Nature Phys. 5, 110–114 (2009); – Gaetan et al., Nature Phys. 5, 115–118 (2009).
• EIT with Rydberg atoms (classical regime, but same idea as this work) – Pritchard et al., PRL 105, 193603 (2010).
• Theory work – Lukin et al., PRL 87, 037901 (2001); – Petrosyan, Otterbach, & Fleischhauer, PRL 107, 213601 (2011); – Gorshkov et al., PRL 107, 133602 (2011); – Muller, Lesanovsky, Weimer, Buechler, & Zoller, PRL 102, 170502 (2009).
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Very strong Rydberg-Rydberg interaction (~THz at 1 µm) prevents excitation of two Rydberg atoms within some blockade radius rb
-> Rydberg slow-light polaritons cannot coexist within rb. Size of Rydberg polariton ~ resonant attenuation length za×√OD -> expect single photon nonlinearity for za < rb, i.e. at high atomic density. Our system: za<2µm rb≥10µm
EIT with interacting Rydberg atoms
~za
rb
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Experimental setup
Crossed dipole trap
Continuous probe and control beams
Small probe waist (4.5 µm)
Photon counters
Interference filter
Ultracold high-density 87Rb ensemble (1012 cm-3) Attenuation length za = 2 µm Rydberg levels nS1/2, n=46…100
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Similar measurements of large optical nonlinearity (in classical regime attenuation length > blockade radius): Pritchard, Maxwell, Gauguet, Weatherill, Jones, and Adams, Phys. Rev. Lett. 105, 193603 (2010).
1 µs-1
2 µs-1
4 µs-1
6 µs-1
|n=100 S1/2⟩ Optical depth OD=40 Attenuation length 2µm Blockade radius 13µm
Rydberg EIT spectra for different probe photon rates
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One-photon transmission and two-photon loss
τ (µs)
T. Peyronel, O. Firstenberg, Q.-Y. Liang, Alexey Gorshkov, T. Pohl, M. Lukin, and V. Vuletic, Nature Advance online publication (7/25/2012).
Blockade radius
n=46 n=100 g2(0)=0.13(2) g2c(0)=0.04(3)
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Propagation of two-excitation wavefunction inside Rydberg EIT medium: theory calculation
Two-photon component
Two-Rydberg component
Broadening of exclusion range during propagation through optically dense medium (OD=50) due to dispersion.
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Detuned EIT: Forces between photons
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Attractive force between two photons
phase
Measured two-photon wavefunction
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Transition from photon antibunching (dissipation) to bunching (forces)
g(2)
=|Ψ
|2
phas
e
Separation time τ
Incident photons linearly polarized, measure correlation function in different polarization bases, quantum state tomography
∆=0
∆=2.3Γ ∆=1.5Γ
∆=1.5Γ
∆=2.3Γ
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Two-photon bound state
Experiment
Simple theoretical picture (Schrodinger equation)
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Future Rydberg polariton research
• Colliding interacting photons: photonic quantum gates?
• Three-photon correlation functions: photonic solitons?
• Tuning the interactions: 1D photon crystal?
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Summary
• Cavity-free quantum nonlinear medium with different response for one and two photons.
• Cavity-based one-photon transistor where one photon can switch 1000 photons.
• Various possible applications: – photonic quantum gates – quantum non-demolition detector for photon – 1D quantum gas of interacting photons (crystal?)