Nonlinear microwave optics in superconducting quantum circuits

Nonlinear microwave optics in superconducting quantum circuits

Zachary Dutton

Raytheon BBN Technologies

BBN collaboratorsThomas OhkiJohn SchlaferBhaskar MookerjiWilliam KellyBlake 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

• Stopped light: Coherent information storage and retreival with an auxiliary laser

– Classical and quantum memory

– Interface between flying and stationary qubits

Hau, et. al Nature (1999)Kash, et. al PRL (1999)

Light at 38 m.p.h. (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)– 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 (~– 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 absorptionThree level EITFour level EIT with switching beam

Schmidt & Imamoglu (Opt. Lett. 1996)Yamamoto & Harris (PRL 1998)

Braje, et. al; PRA (2003)

Progress in coherent NLO

Atomic ensemblesCPT (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)

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

– Increasingly complicated systems

SolidsEIT (MIT/Hanscom 2002)Slow light (MIT/Hanscom 2002, Rochester 2003)Stored light (MIT/Hanscom 2002, Rochester 2003)

Fibers, resonators, bandgapsEIT (IBM 2005, Cornell 2006)Slow light (IBM 2005)Stored light (Cornell 2007)Low light level switching (Cornell 2004)

Quantum WellsEIT (Imperial 2000; Oregon, 2004)Slow light (Oregon, Berkeley 2005)

SuperconductorsAutler-Townes (NIST 2009, ETH 2009)CPT (BBN 2009)EIT (NEC 2010)Optical switching (Chalmers 2011, NIST 2011)

Quantum DotsCPT (Michigan 2008)

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

1

2

Photon entanglement

sourceLehnert, et. al, Nature Physics (2008)

Teleportation circuit

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

?*

Coherent states

SPDC

Target detection error

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

• Coherent population trapping (CPT)– Optical fields drive a three-level

system is driven into a coherent ‘dark state’ superposition

– Dark state is decoupled from the fields due to destructive quantum interference

– Excited state population (ρ22) is suppressed near resonance

10 pcD

p0-1 1

22

0

0.05

pcp

cp

p

H *

*

0

00

0 1

2

pc

p

Coherent Population Trapping

• Coherent population trapping (CPT)– Optical fields drive a three-level

system is driven into a coherent ‘dark state’ superposition

– Dark state is decoupled from the fields due to destructive quantum interference

– Excited state population (ρ22) is suppressed

10 pcD

0-1 1

22

0

0.05

pcp

cp

p

H *

*

0

00

0 1

2

pc = 0.6

p

p

• 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

EIT, slow light, and stored light

1

2

p

0








1

2

p c

0








01

2

p c

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

Laboratory for Bits and Waves

Oxford/Vericold Cryogen-free DR200-1010 mK base with 20 HF lines an 100 DC with 2 SM fibers

Qubit potential for -system

U

φ


U

φ

1 103 0

2 106 0

1 103 0

2 106 0


U

φ

CPT resonance

12012 fff p

12ffc

012 fff cp

0 1

2

fcfp

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

0

1

2

Im(r)Re(r)

Im(r)Re(r)

0

1

2•“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

Ideally one wants the probe absorption line to decay faster than the dark state

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

Nonlinear microwave optics in superconducting quantum circuits

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