DISSIPATION ENHANCED COHERENCE IN SUPERCONDUCTING QUBITS Collaborators Prof. A.N. Korotkov (UCR) Prof. S.M. Girvin (Yale) Dr. Mohan Sarovar (Sandia) Prof. B. Whaley (UCB) IRFAN SIDDIQI CQIQC Seminar March 22, 2013 Quantum Nanoelectronics Laboratory U. Toronto Department of Physics, UC Berkeley
AN INDUSTRY BUILT ON SAND… 1947 Bardeen, Brattain, Shockley 1956 Nobel Prize
Trapped ions QUANTUM BITS quantum energy levels h NV Centers Energy f 1 e Molecules g 0 Quantum Dot Superconducting Circuit • standard nanofabrication • engineered parameters • decoherence (T 1 , T 2 )
THE QUBIT
HOW CAN A SUPERCONDUCTING CIRCUIT BECOME QUANTUM-MECHANICAL AT THE LEVEL OF CURRENTS AND VOLTAGES? SIMPLEST EXAMPLE: SUPERCONDUCTING LC OSCILLATOR CIRCUIT MICROFABRICATION L ~ 3nH, C ~ 10pF, ω r /2 π ~ 1GHz, Q ~ 106
LC OSCILLATOR AS A QUANTUM CIRCUIT E φ + q V - q I ω h r φ [ ] φ = h , q i ω > k T h φ = r B LI 10mK 1GHz = q C V (~ 50mK)
THE JOSEPHSON TUNNEL JUNCTION: NON-LINEARITY AT ITS FINEST! δ I 0 δ = δ I ( ) I sin( ) 0 (NON-LINEAR INDUCTOR) = − h δ δ U ( ) I cos( ) 0 2 e
SUPERCONDUCTING TRANSMON QUBIT LJ ~ 13 nH C ~ 70 fF • Tunable qubit frequency • ω 01 ~ 5-8 GHz J. Koch et al., Physical Review A 76, 042319 (2007)
C Josephson tunnel junctions LJ
THE MEASUREMENT APPARATUS
MEASUREMENT : COUPLE TO E-M FIELD OF CAVITY (Jaynes-Cummings) 1 0 Transmission Cavity Frequency
THE CHALLENGE OF GREGARIOUS QUBITS… Vacuum Fluctuations Circuit Based “Defects” Qubit INFORMATION BACKACTION • Current state of the art (no control): T1, T2 ~ 10-100’s µ s • Active control via engineered dissipation - measurement based feedback (PART I) - quantum bath engineering (PART II)
HOW DO WE STABILIZE AN OSCILLATION? QUANTUM FEEDBACK via WEAK CONTINUOUS MEASUREMENT R. Vijay et al., Nature 490 , 77 (2012).
MEASUREMENT BASED FEEDBACK Vacuum Fluctuations Circuit Based “Defects” Qubit INFORMATION BACKACTION Resonant Cavity CONTROL WEAK MEASUREMENTS TO A. N. Korotkov, PRB 1999 H. M. Wiseman, G. J. Milburn, STABILIZE RABI OSCILLATIONS Cambridge Univ. Press, 2009
INITIAL STATE: |ψ〉 = |0〉 + |1〉 Strong QND Measurement Weak QND Measurement 0 Quantum Co. The Nils Bohr Co. 1 Quantum Co. The Nils Bohr Co.
STRONG MEASUREMENT 1 0 0 Nonuniform Magnetic field 1 Spin ½ Particle Position Atomic Beam Superposition State PROJECTIVE MEASUREMENT: Ψ = α + β 0 1 ABLE TO RESOLVE STATES
WEAK MEASUREMENT 1 0 Nonuniform Magnetic field Spin ½ Particle Position Atomic Beam Superposition State EXTRACT SOME INFORMATION, Ψ = α + β 0 1 BUT NOT ENOUGH TO DETERMINE STATE
“BAD” MEASUREMENT 1 0 0 Nonuniform Magnetic field 1 Spin ½ Particle Position Atomic Beam Superposition State PROJECTIVE MEASUREMENT BUT Ψ = α + β 0 1 CAN’T RESOLVE POINTER STATES
MEASUREMENT: COUPLE TO E-M FIELD OF CAVITY (Jaynes-Cummings) 1 0 VARY MEASUREMENT STRENGTH Cavity USING DISPERSIVE SHIFT & Transmission PHOTON NUMBER NEED TO DETECT ~ SINGLE MICROWAVE PHOTONS in T1 ~ µ s Frequency
THE AMPLIFIER
PARAMETRIC AMPLIFICATION LJ ~ 0.1 nH C ~ 10000 fF 2 / 2 ) e Ω 0 I h ( U 0 M. J. Hatridge et al., Phys. Rev . B 83 , 134501 (2011)
PARAMETRIC AMPLIFICATION ω idler ω pump ω pump Non-linear Medium ω signal ω signal ω pump = ω signal + ω idler 2ω pump = ω signal + ω idler
Tunnel Al Lumped LC SQUID Resonator junction 4-8 GHz Coupled to 50 Ω Q = 26 Nb 4 µ m ground plane Flux line Capacitor Capacitor M. Hatridge et al., Phys. Rev . B 83 , 134501 (2011) 100 µ m
EXPERIMENTAL SETUP OUTPUT INPUT DRIVE
SINGLE SHOT MEASUREMENT TRACES qubit cavity (π, 2π) 1 0 SEMICONDUCTOR HEMT AMPLIFIER JOSEPHSON PARAMETRIC AMPLIFIER R. Vijay et al., Phys. Rev. Lett. 106 , 110502 (2011)
RABI OSCILLATIONS No Measurement Weak Measurement Strong Measurement • Noisy detector output <-> Random evolution of qubit • Stabilize oscillatory motion (eg. Rabi Oscillations) by locking to a classical clock A. N. Korotkov, Phys. Rev. B 60, 5737 (1999) A. Frisk Kockum, L. Tornberg, and G. Johansson, arXiv:1202.2386v2 C. Sayrin et al., Nature 477 , 73 (2011) A. Palacios-Laloy et al., Nature Phys. 6 , 442 (2010) H. M. Wiseman, G. J. Milburn, Quantum Measurement and Control, (Cambridge Univ. Press, 2009)
RABI OSCILLATIONS with CONTINUOUS STRONG MEASUREMENT turn on Rabi drive • Continuously drive qubit Γ ↓ Γ ↑ • Continuously measure • Display single measurement Strong Measurement Pins Qubit
QUANTUM ZENO EFFECT ( Γ ↑ + Γ ↓ ) / ν Rabi transitions suppressed n W. M. Itano et al., Phys. Rev . A 41 , 2295 (1990) J. Gambetta et al., Phys. Rev . A 77 , 012112 (2008)
VARYING MEASUREMENT STRENGTH = n 35 (0, π) 1 0 = n 20 τ = 400 ns = • Integrate measurement trace n 10 for 400 ns • Repeat and histogram = n 2 • ~ 2x quantum noise floor
RABI OSCILLATIONS with CONTINUOUS WEAK MEASUREMENT: ENSEMBLE AVERAGE • Continuously drive qubit • Continuously measure (weakly) • Repeat • Display average Each individual trace has random, measurement induced phase jitter
STABILIZING A QUANTUM “VOLTAGE CONTROLLED OSCILLATOR” Phase locked loop (PLL) Drive Oscillator ( ω 01 ) Feedback on A to synchronize with reference Quantum VCO Ω R(A) A (qubit Rabi flopping) Comparator
STABILIZED RABI OSCILLATIONS Feedback OFF Feedback ON
STILL GOING… • Single quadrature measurement • Operate with measurement dephasing dominant • Appearance of narrow peak when PLL operational
REPHASING THE QUBIT Start Rabi Oscillations Perform tomography Turn on Feedback Measurement induced dephasing
STATE TOMOGRAPHY • Observe expected rotation in the X,Z plane • Observe Bloch vector reduced to 50% of maximum
FEEDBACK EFFICIENCY 2 = D Γ Ω 1 F / + R η Γ Ω / F R D: “feedback efficiency” F: feedback strength η : detector efficiency (0-1) Γ : dephasing rate Ω R : Rabi frequency (A.N. Korotkov) • Analytics do not include delay time, finite bandwidth, T 1 • Numerics include delay and bandwidth good agreement
CAN WE OBSERVE THE “PHYSICAL” EFFECTS OF SQUEEZED VACUUM? SUPPRESSION OF THE RADIATIVE DECAY OF ATOMIC COHERENCE IN SQUEEZED VACUUM K. Murch et al., arXiv: 1301.6276
QUANTUM BATH ENGINEERING: SQUEEZING Vacuum Fluctuations Circuit Based Parametric Qubit Amplifier Resonant Cavity Slusher et al, PRL 1985 SQUEEZED LIGHT / MATTER INTERACTION Treps et al, PRL 2002 MODIFIES TRANSVERSE/LONGITUDINAL DECAY Gardiner, PRL 1986
T 1 = 560 ns T 2 *= 1080 ns (polariton regime)
SQUEEZING MOMENTS
RAMSEY WITH GAUSSIAN FLUCTUATIONS
RAMSEY WITH GAUSSIAN FLUCTUATIONS
RAMSEY WITH SQUEEZED FLUCTUATIONS
QUBIT ENABLED RECONSTRUCTION OF AN ITINERANT SQUEEZED STATE
ROTATING THE SQUEEZER
HOW EFFICIENT IS THE SQUEEZING?
FUTURE DIRECTIONS • QUANTUM FEEDBACK/CONTROL - OPTIMIZE EFFICIENCY - FULL BAYESIAN FEEDBACK - GENERATION/STABILIZATION OF ENTANGLED STATES • MULTIPLEXED QUBIT READOUT • ON-CHIP PARAMPS - BACKACTION OF NONLINEAR TANK CIRCUIT - TRANSMISSION LINE AMPLIFIERS
QNL Dr. Kater Murch Dr. Andrew Schmidt Dr. Shay Hacohen-Gourgy Dr. Nico Roch Eli Levenson-Falk Edward Henry Chris Macklin Natania Antler Steven Weber Andrew Eddins Mollie Schwartz Daniel Slichter (NIST) Michael Hatridge (Yale) Anirudh Narla (Yale) Zlatko Minev (Yale) Yu-Dong Sun Ravi Naik (U. Chicago) Dr. R. Vijay (TIFR) Seita Onishi (UC Berkeley) Dr. Ofer Naaman (Grumann)
HOW DO WE STABILIZE A SUPERPOSITION ? CAVITY ASSISTED QUANTUM BATH ENGINEERING K. Murch et al., Phys. Rev. Lett. 109 , 183602 (2012)
QUANTUM BATH ENGINEERING: COOLING Vacuum Fluctuations Circuit Based Qubit Resonant Cavity Poyatos, Zoller (1996) Lutkenhaus (1998) Wiseman (1994) Kraus (2008) Diehl (2008,2010) AUTONOMOUSLY COOL TO ANY Schirmer (2010) Wang (2001,2005) ARBITRARY STATE ON THE BLOCH SPHERE Carvalho (2007, 2008) Marcos (2012)
QUANTUM RESERVOIR: SHOT NOISE IN DRIVEN CAVITY ∆ C = + κ ∆ C = − κ 3 3 ω d ω C ∆ = ω − ω Noise peaks at ω < 0 C d C ∆ C > 0 : Cavity emits heating ∆ C < Noise peaks at ω > 0 0 : Cavity absorbs cooling A.A. Clerk et al., Rev. Mod. Phys 82, 1155 (2010)
CAVITY ASSISTED COOLING g − e − = • Drive qubit at ω q (on resonance) 2 • Ω R / 2 π ~ 10 MHz thermal state • Apply additional tone at ω d (red detuned) • Cavity enhances anti-Stokes response g + e + = cool thermal state to |+> 2
BUILDING UP COHERENCE • Conventional Ramsey experiment - T2* = 4.9 µ s ; 40% contrast • Apply tone at qubit frequency ω q’ & ω d (∆ C = −Ω R ) • Cool for a variable cooling time • π /2 pulse slightly detuned from ω q’ waiting time • Oscillations persist indefinitely
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