Nonlinear microwave optics in superconducting quantum circuits

1
Nonlinear microwave optics in superconducting
quantum circuits

• Zachary Dutton
• Raytheon BBN Technologies

BBN collaborators Thomas Ohki John
Schlafer Bhaskar Mookerji William Kelly Blake
Johnson
NIST collaborators Jeffery Kline David
Pappas Martin Weides
2
Slow and stopped light

• Slow light Controlling optical pulse propagation
  through atom clouds with auxiliary laser
• Now implemented in multiple other systems
• All optical buffer
• Stopped light Coherent information storage and
  retreival with an auxiliary laser
• Classical and quantum memory
• Interface between flying and stationary qubits

Light at 38 m.p.h.
(Harvard 2003, CalTech 2005, GaTech 2005)
Hau, et. al Nature (1999) Kash, et. al PRL (1999)
3
Low light level NLO in atoms

• Atomic slow light and stored light are based on
  electromagnetically induced transparency (EIT)
• Sensitive coherent interference effect
• This sensitivity can be exploited for low light
  level nonlinear optics
• Optical switching
• Theoretically can be done with as few as 1
  photon per cross-section (l2)
• Demonstrated at 23 photons
• Giant Kerr nonlinearity
• As few as 1 photon in one field can exhibit large
  phase shift on a photon of another field
• All optical quantum processing

Schmidt Imamoglu (Opt. Lett. 1996) Yamamoto
Harris (PRL 1998)
Braje, et. al PRA (2003)
Two level absorption Three level EIT Four level
EIT with switching beam
4
Progress in coherent NLO

• The last 12 years have seen remarkable progress
  in two senses
• Increasingly complicated EIT based NLO
  experiments
• Increasingly complicated systems

Atomic ensembles CPT (Pisa 1976) EIT (Stanford
1991) Slow light (Stanford 1995,
Harvard 1999, Texas AM 1999) Stored light
(Harvard 2001) Low light level switching
(Stanford 2003) Single photon storage
(Harvard 2003, CalTech 2005, GaTech
2005) Entanglement generation swapping
(CalTech 2007, GaTech 2007)
Solids EIT (MIT/Hanscom 2002) Slow light
(MIT/Hanscom 2002, Rochester 2003) Stored light
(MIT/Hanscom 2002, Rochester 2003)
Fibers, resonators, bandgaps EIT (IBM 2005,
Cornell 2006) Slow light (IBM 2005) Stored light
(Cornell 2007) Low light level switching
(Cornell 2004)
Superconductors Autler-Townes (NIST 2009, ETH
2009) CPT (BBN 2009) EIT (NEC 2010) Optical
switching (Chalmers 2011, NIST 2011)
Quantum Wells EIT (Imperial 2000 Oregon,
2004) Slow light (Oregon, Berkeley 2005)
Quantum Dots CPT (Michigan 2008)
5
Distributed entanglement for QC

• Superconducting qubits are a strong candidate for
  scalable, fast quantum processing
• Long distance processing both within and between
  quantum processing units can be accomplished via
  shared entanglement LOCC
• Requires microwave photon entanglement sources
  and quantum memory

Photon entanglement source
Lehnert, et. al, Nature Physics (2008)
Teleportation circuit
6
Quantum Illumination

• Quantum illumination is an interesting new use of
  entanglement
• SNR improved by use of joint detection of signal
  and idler
• Improves target detection in lossy and noisy
  (entanglement breaking) channels
• Also can be used for secure comm
• Experiments underway at MIT
• The advantage may be most pronounced for
  microwaves (i.e. quantum radar)
• 100 photons/mode versus 10-6 at optical
  frequencies
• The idler requires a tunable delay

Target detection error
Coherent states
SPDC
Lloyd (Science 2008) Tan (PRL 2009) Shapiro (PRA
2010)
7
CPT in superconducting circuits

• Superconducting quantum circuits consist of
  quantized phase states
• Proposed coherent population trapping (CPT) using
  three quantized levels of superconducting flux
  qubit
• Sensitive quantum interference shown to be
  sensitive probe of decoherence

8
Coherent Population Trapping

• Coherent population trapping (CPT)
• Optical fields drive a three-level L system is
  driven into a coherent dark state superposition
  
• Dark state is decoupled from the fields due to
  destructive quantum interference
• Excited state population (?22) is suppressed near
  resonance

0.05
0
1
-1
0
9
Coherent Population Trapping

• Coherent population trapping (CPT)
• Optical fields drive a three-level L system is
  driven into a coherent dark state superposition
  
• Dark state is decoupled from the fields due to
  destructive quantum interference
• Excited state population (?22) is suppressed

0.05
0
1
-1
0
10
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
11
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
12
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
13
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
14
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
15
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
16
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
17
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
18
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
19
EIT, slow light, and stored light

• Back action of matter on light fields
• Transparency of light fields on resonance
• By Kramers-Kronig, there is a steep linear
  dispersion, causing slow light
• Stored light
• Dynamical control of coupling field can store
  photonic information (quantum or classical) in
  spins of matter field
• Further applications
• Kerr nonlinearity, processing, low light-level
  optical switching, lasing without inversion

Wp
Wc
20
Laboratory for Bits and Waves

• State of the art superconducting lab facility
  came online in 2009

Oxford/Vericold Cryogen-free DR200-10 10 mK base
with 20 HF lines an 100 DC with 2 SM fibers
21
Laboratory for Bits and Waves

• State of the art superconducting lab facility
  came online in 2009

Oxford/Vericold Cryogen-free DR200-10 10 mK base
with 20 HF lines an 100 DC with 2 SM fibers
22
Qubit potential for L-system
U
f
23
Qubit potential for L-system
?
U
f
24
Qubit potential for L-system
U
f
25
Qubit potential for L-system
?2? 106 ?0
?1? 103 ?0
U
f
26
Qubit potential for L-system
?2? 106 ?0
?1? 103 ?0
U
f
27
CPT resonance
fc
fp
W. R. Kelly, Z. Dutton, J. Schlafer, B. Mookerji,
T. A. Ohki, J. S. Kline, D. P. Pappas, PRL (2010)
28
CPT time dynamics

• Murali et. al. PRL (2004) predicted that CPT
  could be used as a decoherence probe

W. R. Kelly, Z. Dutton, J. Schlafer, B. Mookerji,
T. A. Ohki, J. S. Kline, D. P. Pappas, PRL (2010)
29
EIT experiment

• NEC group recently measured the probe
  transmission and phase shift in a transmission
  line coupled to a qubit
• Traced out the real and imaginary susceptibility
• Done in a strongly dampled (T1 limited) device,
  which maximizes the nonlinearity

Abdumalikov, et. al (Science 2011)
30
Switching
Li, et. al (arXiv 1103.2631)
Hoi , et. al (PRL 2011)

• Unlike atomic systems, superconducting EIT is
  done in a 1D transmission line geometry
• Absorption and scattering is then replaced by
  reflection in the line
• Chalmers group used EIT a circulator to show a
  switch

31
CPT vs AT
Ideally one wants the probe absorption line to
decay faster than the dark state

• Lambda configuration allows and coupling field
  broadened EIT resonance
• Quantum interference CPT regime
• Larger nonlinearities

• Ladder is dark state decay limited
• Autler-Townes splitting regime
• Smaller nonlinearities

2G
2G
G
G
Im(r) Re(r)
Im(r) Re(r)
32
Slow light simulations

• To get a large nonlinearity one ideally needs a
  large optical density
• Larger delay-bandwidth products (D1/2)
• Needed to store entire pulse in the medium (Dgtgt1)
• In our context, this means coupling multiple
  qubits to transmission line
• Also need T1 limited device and coupling field
  broadened resonance

reference
1 qubit
8 qubits
33
Summary and outlook

• EIT based effects lead to an interesting variety
  of low light level coherent NLO applications
• Light buffers, classical and quantum memories,
  optical switching, Kerr nonlinearity
• Quantum optics is now being done in
  superconducting quantum circuits
• CPT, EIT, squeezed photon sources
• Important development for quantum processing
  protocols, quantum illuminati
• Slow and stopped light may be next on the horizon