Nonlinear microwave optics in superconducting quantum circuits

1. Nonlinear microwave optics in superconducting quantum circuits Zachary Dutton Raytheon BBN Technologies NIST collaborators Jeffery Kline David Pappas Martin Weides BBN collaborators Thomas Ohki John Schlafer Bhaskar Mookerji William Kelly Blake Johnson

2. Slow and stopped light Light at 38 m.p.h. (Harvard 2003, CalTech 2005, GaTech 2005) Hau, et. al Nature (1999) Kash, et. al PRL (1999) • 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

3. Low light level NLO in atoms 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 • 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

4. Progress in coherent NLO 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) 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) • The last 12 years have seen remarkable progress in two senses • Increasingly complicated EIT based NLO experiments • Increasingly complicated systems

5. Distributed entanglement for QC 1 2 Photon entanglement source Lehnert, et. al, Nature Physics (2008) 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 Teleportation circuit

6. Quantum Illumination * ? Target detection error Coherent states SPDC Lloyd (Science 2008) Tan (PRL 2009) Shapiro (PRA 2010) • 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

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 g Dp Wc Wp 0.05 0 1 -1 0 • 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 (ρ22) is suppressed near resonance

9. Coherent Population Trapping g Dp Wc = 0.6 g Wp 0.05 0 1 -1 0 • 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 (ρ22) is suppressed

10. EIT, slow light, and stored light Wp • 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

11. EIT, slow light, and stored light Wp Wc • 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

12. EIT, slow light, and stored light Wp Wc • 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

13. EIT, slow light, and stored light Wp Wc • 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

14. EIT, slow light, and stored light Wp Wc • 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

15. EIT, slow light, and stored light Wp Wc • 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

16. EIT, slow light, and stored light Wp Wc • 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

17. EIT, slow light, and stored light Wp Wc • 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

18. EIT, slow light, and stored light Wp Wc • 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

19. EIT, slow light, and stored light Wp Wc • 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

20. Laboratory for Bits and Waves Oxford/Vericold Cryogen-free DR200-10 10 mK base with 20 HF lines an 100 DC with 2 SM fibers State of the art superconducting lab facility came online in 2009

21. Laboratory for Bits and Waves Oxford/Vericold Cryogen-free DR200-10 10 mK base with 20 HF lines an 100 DC with 2 SM fibers State of the art superconducting lab facility came online in 2009

22. Qubit potential for L-system U φ

23. Qubit potential for L-system  U φ

24. Qubit potential for L-system U φ

25. Qubit potential for L-system 2 106 0 1 103 0 U φ

26. Qubit potential for L-system 2 106 0 1 103 0 U φ

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 (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

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