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
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
•
Light at 38 m.p.h.
Hau, et. al Nature (1999)
Kash, et. al PRL (1999)
Stopped light:
Coherent information
storage and retreival with
an auxiliary laser
– Classical and
quantum memory
– Interface between
flying and stationary
qubits
(Harvard 2003, CalTech 2005,
GaTech 2005)
Low light level NLO in atoms
• Atomic slow light and stored
light are based on
electromagnetically induced
transparency (EIT)
Schmidt & Imamoglu (Opt. Lett. 1996)
Yamamoto & Harris (PRL 1998)
– Sensitive coherent interference effect
– This sensitivity can be exploited for
low light level nonlinear optics
•
Optical switching
Braje, et. al; PRA (2003)
– 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
Two level
absorption
Three level EIT
Four level EIT with
switching beam
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 A&M 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)
Superconductors
Autler-Townes (NIST 2009, ETH 2009)
CPT (BBN 2009)
EIT (NEC 2010)
Optical switching (Chalmers 2011,
NIST 2011)
Fibers, resonators,
bandgaps
EIT (IBM 2005, Cornell 2006)
Slow light (IBM 2005)
Stored light (Cornell 2007)
Low light level switching
(Cornell 2004)
Quantum Wells
Quantum Dots
CPT (Michigan 2008)
EIT (Imperial 2000; Oregon, 2004)
Slow light (Oregon, Berkeley 2005)
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
1
2
Photon
entanglement
source
• Requires microwave photon
entanglement sources and
quantum memory
Teleportation circuit
Lehnert, et. al,
Nature Physics
(2008)
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
*
?
Target detection error
Coherent states
SPDC
• 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
Lloyd (Science 2008)
Tan (PRL 2009)
Shapiro (PRA 2010)
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
Coherent Population Trapping
 0

H  0

 p
0
p
c
*p 

*
c 
 p 
• Coherent population trapping
(CPT)
2
– Optical fields drive a three-level L
0.05
system is driven into a coherent
‘dark state’ superposition
D  c 0   p 1 ) 
– Dark state is decoupled from the
fields due to destructive quantum
interference
– Excited state population (ρ22) is
suppressed near resonance

p
p
0
c
1
22
0
-1
0
p 
1
Coherent Population Trapping
 0

H  0

 p
0
p
c
*p 

*
c 
 p 
• Coherent population trapping
(CPT)
2
– Optical fields drive a three-level L
0.05
system is driven into a coherent
‘dark state’ superposition
D  c 0   p 1 ) 
– Dark state is decoupled from the
fields due to destructive quantum
interference
– Excited state population (ρ22) is
suppressed

c = 0.6 
p
p
0
1
22
0
-1
0
p 
1
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
2
p
0
• 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
1
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
2
p
0
• 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
c
1
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
2
p
0
• 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
c
1
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
2
p
0
• 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
c
1
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
2
p
0
• 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
c
1
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
2
p
0
• 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
c
1
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
2
p
0
• 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
c
1
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
2
p
0
• 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
c
1
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
2
p
0
• 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
c
1
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
2
p
0
• 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
c
1
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
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
Qubit potential for L-system
U
φ
Qubit potential for L-system

U
φ
Qubit potential for L-system
U
φ
Qubit potential for L-system
2 106 0
1 103 0
U
φ
Qubit potential for L-system
2 106 0
1 103 0
U
φ
CPT resonance
2
fc
fp
0
1
2 f p  f 01  f12
f c  f12
2 f p  f c  f 01
W. R. Kelly, Z. Dutton, J. Schlafer, B. Mookerji, T. A.
Ohki, J. S. Kline, D. P. Pappas, PRL (2010)
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)
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)
Switching
•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
Hoi , et. al
(PRL 2011)
Li, et. al (arXiv
1103.2631)
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
Im(r)
Re(r)
2
2
1

•“Ladder” is dark
state decay limited
•“Autler-Townes
splitting” regime
•Smaller
nonlinearities
0
2
2
1

0
Im(r)
Re(r)
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 (D>>1)
•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
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