JOSEPHSON-BASED PARAMETRIC AMPLIFIERS FOR QUANTUM MEASUREMENTS

Transcription

1 JOSEPHSON-BASED PARAMETRIC AMPLIFIERS FOR QUANTUM MEASUREMENTS QUAN ELEC RONICS UM MECHANICAL LAB Applied Physics and Physics, Yale University N. BERGEAL (ESPCI Paris) F. SCHACKERT* A. KAMAL B. HUARD (ENS Paris) A. MARBLESTONE R. VIJAY (U.C.Berkeley) I. SIDDIQI (U.C.Berkeley) C. RIGETTI M. METCALFE V. MANUCHARIAN* N. MASLUK M. BRINK K. GEERLINGS L. FRUNZIO M. D. Acknowledgments: R. Schoelkopf, S. Girv, D. Prober * see poster W.M. KECK Heraeus445 Nov 9

2 OUTLINE 1. Introduction and motivation. Basic concepts of quantum signal description 3. Degenerate vs non-degenerate parametric amplifiers 4. Amplifier based on Josephson rg modulator 5. Squeezg 6. Lk with microwave SQUID, conclusions and perspectives

3 PROBLEM: AMPLIFICATION IS NEEDED TO INCREASE ENERGY OF MEASURED SIGNAL, BUT IT ALWAYS DEGRADES INFORMATION RADIO-FREQUENCY PHENOMENON (MHz-GHz) Determistic signal AMP LIFIER DATA PROCESS STAGE DETER tic SIGNAL + + NOISE SIGNAL Noise signal from source (thermal and/or quantum fluctuations) energy source + ADDED NOISE (S/N) out EFFICIENCY = = (S/N) INPUT NOISE INPUT NOISE + ADDED NOISE Applications: Readout of qubits THz photon detection Electrical metrology

4 QUANTUM REGIME: ENERGY OF EACH MODE OF SIGNAL AND THERMAL NOISE IS OF ORDER 1 PHOTON INPUT AT T=: EFFICIENCY = A Caves' added photon number

5 AN IMPROVEMENT BY A FACTOR OF N IN EFFICIENCY TRANSLATES IN AN IMPROVEMENT BY A FACTOR OF N IN MEASUREMENT TIME!

6 THE PROBLEM OF HEAT ENGINES EFFICIENCY GAVE BIRTH TO THERMODYNAMICS η < η = THEOR. T HOT T T HOT COLD Sadi Carnot "Réflexions sur la puissance motrice du feu" (184) THE PROBLEM OF AMPLIFIER EFFICIENCY OPENS A NEW AREA OF NON-EQUILIBRIUM QUANTUM STATISTICAL PHYSICS

7 DISPERSIVE QUBIT READOUT STRATEGY Blais et al. PRA 4, Walraff et al., Nature 4 rf signal ωr ω 1 narrow band-pass filter or 1 rf signal out its phase is poter variable filter QUBIT CIRCUIT filter narrow band-pass filter QUBIT STATE ENCODED IN PHASE OF OUTGOING SIGNAL, NO ENERGY DISSIPATED ON-CHIP A) SHELTER QUBIT FROM ALL RADIATION EXCEPT READOUT ω r B) AMPLIFY OUTGOING SIGNAL WITH LOWEST ADDED NOISE C) SEND ENOUGH PHOTONS TO BEAT ADDED NOISE

8 DISPERSIVE READOUT OF SUPERCONDUCTING QUBITS Josephson qubit CHIP circulator amplifiers ADC λ/ filter IN/OUT ~ mixer microwave generator for readout

9 EXCITATION OF QUBIT IS OFF-RESONANT Josephson qubit CHIP circulator amplifiers ADC IN/OUT ~ mixer ~ microwave generator for qubit excitation

10 READOUT PROTOCOL: EXCITATION OF QUBIT Josephson qubit CHIP circulator amplifiers ADC IN/OUT ~ mixer or 1 ~

11 PRINCIPLE OF DISPERSIVE READOUT Josephson qubit circulator amplifiers CHIP ADC IN/OUT ~ mixer microwave generator for readout frequency f phase shift (deg) -36 width determed by resonator Q 1 f r QND! f

12 TOWARDS OBSERVATION OF BLOCH OSCILLATIONS Zor, Aver and Likharev (1985) very large ductance JJ array Effective sgle JJ I f ~ λ /4 sidebands of readout lear microwave readout Δ f = I e

13 TOWARDS OBSERVATION OF BLOCH OSCILLATIONS Zor, Aver and Likharev (1985) NOW EXISTS! See poster I very large ductance JJ array Effective sgle JJ f ~ λ /4 sidebands of readout lear microwave readout Δ f = I e

14 . Basics of quantum signal description

15 INCOMING AND OUTGOING SIGNAL AMPLITUDES ( ) A x v t p ( + ) A x v t p A = Z c WATTS, v p x I(x) V(x) x V = V + V = Z c A + 1 I = I I = A Z c A location x and time t 1 A = x v p solution: t A (, ) = ( p ) A xt A x vt Z c V = = I V I A x frequency doma: idω / vp [ ω] = e A [ ω] x+ d

16 SIGNAL MODE DESCRIPTION INVOLVES (i) A SPATIAL PART... port 1 port... port l

17 ... AND (ii) A TEMPORAL PART τ center time pτ, center frequency wavelet basis mb + () () example: local cose basis Coifman & Meyer '91 w t w t dt = δ δ pm pm ' ' m m' p p' "MODE AMPLITUDE" IS CONTENT OF THE TILE: Tilg of t-ω plane with basis of orthonormal functions: angular frequency ω a mp + dω = w ω mp [ ω] A[ ω] m b ω = bτ = π τ p time t

18 GEOMETRIC REPRESENTATION OF SIGNAL MODE out-phase amplitude comp nent Im a mp = a μ N noise fuzz disc (diam.= σ Ν ) θ -phase amplitude comp nent Re a mp = a μ N = signal mode energy photon number = signal mode phase θ FRESNEL VECTOR FRESNEL "LOLLYPOP" Classical Quantum: a μ aˆ μ σ = N 1 ω coth μ kt B

19 QUANTUM LIMITED AMPLIFICATION WITH A LINEAR, PHASE-PRESERVING AMPLIFIER IN a μ ' OUT G A + 1 a μ N 1 GN A m = 1 θ a μ θ a μ ' μ = mode dex (l,m,p) STANDARD QUANTUM LIMIT: AMPLIFIER ADDS ONLY ANOTHER ½ PHOTON OF NOISE! MINIMUM REQUIRED BY Q.M. FOR A MEASUREMENT OF BOTH QUADRATURES Shimoda, Takahasi and Townes, J. Phys. Soc. Jpn. 1, 686 (1957); Haus and Mullen, Phys. Rev. 18, 47 (196); Caves, Phys. Rev. D 6, 1817 (198)

20 AMPLIFICATION AT THE QUANTUM LIMIT WITH A LINEAR, PHASE-SENSITIVE AMPLIFIER IN OUT a μ a μ ' de-amplification N 1 N ' N θ a μ amplification a μ ' μ = mode dex (l,m,p) QUANTUM LIMIT : NO ADDED NOISE (!) + SQUEEZING OF QUANTUM FLUCTUATIONS (Caves, 198)

21 QUANTUM OPTICS QUANTUM RF CIRCUITS FIBERS, BEAMS BEAM-SPLITTERS MIRRORS LASERS PHOTODETECTORS ATOMS ~ TRANSM. LINES, WIRES COUPLERS CAPACITORS GENERATORS AMPLIFIERS JOSEPHSON JUNCTIONS COULD WE BUILD AN IDEAL RF PHOTOMULTIPLIER WITH A QUANTUM LIMITED AMPLIFIER FOLLOWED BY AN IDEAL SQUARE LAW DETECTOR?

22 RELATIONSHIP BETWEEN PHASE-PRESERVING AND PHASE-SENSITIVE AMPLIFICATION ϕ ϕ + π/

23 3. Degenerate versus non-degenerate parametric amplification

24 MICROWAVE AMPLIFIER CHARACTERISTICS REPRESENTATION OF MATCHED -PORT AMPLIFIER P ideal circulator ideal coupler noiseless amplifier 1-port G POWER (DC or RF) P out ideal circulator T backaction hot loads T added Power ga ( G = P out /P ) Signal bandwidth B Noise temperature T N =T added Backaction T backaction Dynamic range Tung bandwidth Directionality

25 MICROWAVE AMPLIFIER CHARACTERISTICS REPRESENTATION OF MATCHED -PORT AMPLIFIER P ideal circulator ideal coupler noiseless amplifier 1-port G POWER (DC or RF) P out ideal circulator T backaction hot loads T added Power ga ( G = P out /P ) Signal bandwidth B Noise temperature T N =T added Backaction T backaction Dynamic range Tung bandwidth Directionality OUR MAIN GOAL: UNDERSTAND AND OPTIMIZE TRADE-OFFS STABILITY vs GAIN & BANDWIDTH BANDWIDTH vs GAIN DYNAMIC RANGE vs GAIN ETC...

26 CRYOELECTRONIC PHASE PRES VING AMPLIFIERS POWERED BY DC type kt N /( ω/) A power ga out-of-band back-action noise ease of implem tion HEMT -FET dB small commercial μw SQUID 1- -3dB concern OK RF-SET 1-1- db concern OK QPC 1 ~db very small difficult HEMT: High Electron Mobility Transistor, SET: Sgle Electron Transistor, QPC: Quantum Pot Contact

27 CAN WE REACH QUANTUM LIMIT WITH SUFFICIENT GAIN AND BANDWIDTH, WHILE PRODUCING MINIMAL BACKACTION? PARAMETRIC AMPLIFICATION WITH JOSEPHSON CIRCUITS Yurke et al, Phys. Rev. A 39, 519 (1989) Tholen et al., Appl. Phys. Lett. 9, 5359, (7) Castellanos-Beltran and Lehnert, Appl. Phys. Lett. 91, 8359 (7) Yamamoto et al. Appl. Phys. Lett 93, 451 (8) Bergeal et al. arxiv:85.345v1 (8) to appear Nature Physics Spietz, Irw and Aumentado, APL 93, 856 (8) Clerk et al., to appear Review of Modern Physics (8) Abdo et al., arxiv:811:571; Eur. Phys. Lett. 85, 681 (9) Sandberg et al., arxiv: v1, Appl. Phys. Lett. 9, 351 (8)

28 PARAMETRIC AMPLIFICATION PRINCIPLE IN THE SCATTERING LANGUAGE ω pump ω pump ω signal Purely Dispersive Non-lear Medium ω signal (no signal) ω idler ω idler

29 PARAMETRIC AMPLIFICATION PRINCIPLE IN THE SCATTERING LANGUAGE ω pump ω pump ω signal Purely Dispersive Non-lear Medium ω signal (no signal) ω idler ω idler ω + ω = ω signal idler pump ω + ω = ω signal idler pump "3-wave process" "4-wave process"

30 HAVEN'T WE SAID WE WERE DEALING WITH A LINEAR AMPLIFIER? FOR LARGE PUMP AMPLITUDES AND LOW PUMP DEPLETION, THE BASIC NON-LINEAR WAVE-MIXING PROCESSES APPEAR AS LINEAR SCATTERING PROCESSES FROM THE POINT OF VIEW OF SIGNAL AND IDLER MODES

31 JOSEPHSON TUNNEL JUNCTION PROVIDES A NON-LINEAR INDUCTOR WITH NO DISSIPATION 1nm S I S superconductorsulatorsuperconductor tunnel junction L J C J Ι φ t ( ') = V t dt ' Ι I Ι = φ / L J L J φ = I φ ( ) I = I s φ / φ φ = e

32 BASIC PROCESS: 4-WAVE MIXING φ I ( ) δ L I J E J L J L J = = E ( e) ei LJ I δ LJ = ( I I) 6 I Kerr J

33 BASIC PROCESS: 4-WAVE MIXING ω 1 ω 3 φ I ( ) δ L I J ω ω 4 ω1+ ω = ω3+ ω4 E J L J L J = = E ( e) ei LJ I δ LJ = ( I I) 6 I J

34 BASIC PROCESS: 4-WAVE MIXING ω 1 ω 3 φ I ( ) δ L I J ω ω 4 ω1+ ω = ω3+ ω4 E J L J L J = = E ( e) ei LJ I δ LJ = ( I I) 6 I J ω 1 ω 3 ω1 = ω + ω3+ ω4 ω 4 ω

35 BASIC PROCESS: 4-WAVE MIXING ω 1 ω 3 φ I ( ) δ L I J ω ω 4 ω1+ ω = ω3+ ω4 E J L J L J = = E ( e) ei LJ I δ LJ = ( I I) 6 I J one wave can be at ω= (DC bias) ω 1 ω 3 ω1 = ω + ω3+ ω4 3-wave mixg ω 4 ω

36 BASIC PROCESS: 4-WAVE MIXING ω 1 ω 3 φ I ( ) δ L I J ω ω 4 ω1+ ω = ω3+ ω4 E J L J L J = = E ( e) ei LJ I δ LJ = ( I I) 6 I J ω 1 ω 3 ω1 = ω + ω3+ ω4 ω 4 ω If current I too large, more exotic, less controllable processes!

37 TWO TYPES OF PARAMETRIC AMPLIFIERS signal mode = idler mode degenerate paramp. phase-sensitive (1-mode squeezg) signal mode idler mode non-degenerate paramp. phase-preservg (-mode squeezg)

38 DEGENERATE PARAMP AS SIMPLEST EXAMPLE OF ACTIVE LINEAR, DISPERSIVE 1-PORT Just take a L and a C (pure dispersive elements, no ternal dissipation) PASSIVE A ( t) ACTIVE A ( t) L C Zc C Zc ω = 1 LC out A ( t) out A ( t) ( ) = +ε ( ω ) L t L[1 cos t ]

39 PARAMETRIC ALLY PUMPED OSCIL LATORS MECHANICAL SYSTEM ω ω PUMP: WORK AGAINST CENTRIFUGAL FORCE

40 PARAMETRIC ALLY PUMPED OSCIL LATORS ELECTRICAL SYSTEM RF FLUX BIASED DC SQUID (3W) ( ) = + s ( ω ) I t I I t B B P (NEC, Chalmers)

41 PARAMETRIC ALLY PUMPED OSCIL LATORS ELECTRICAL SYSTEM RF FLUX BIASED DC SQUID (3W) ( ) = + s ( ω ) I t I I t B B P (NEC, Chalmers) RF BIASED JUNCTION (4W) EFFECTIVE PARAMETRIC DRIVE ( t) = A ( t) + cos( ω ) A S AP t INDIRECT PARAMETRIC ω (Yale, NIST KTH, Berkeley)

42 DEGENERATE PARAMETRIC PUMPING 1 INTERNAL MODE ω = resonant frequency IN ω S ω I ω I ωs ω OUT ω S ω I ωi ωs ω Pump frequency Ω = p ω

43 MINIMAL IMPLEMENTATION OF PHASE-PRES VING PARAMETRIC AMPLIFIER COUPLED OSCILLATORS WITH ACCESS PORTS... M ωa ωb

44 MINIMAL IMPLEMENTATION OF PHASE-PRES VING PARAMETRIC AMPLIFIER TIME-DEPENDENT COUPLING BETWEEN ( ) THE OSCILLATORS 1 cos P a1 () t M = M + ε Ω t ωa ωb ( ) a t = out a ( t ) a ( t) out 1 SIGNAL PORT IMAGE (OR "IDLER") PORT Ω = ω + ω p 1 PUMP

45 MINIMAL IMPLEMENTATION OF PHASE-PRES VING PARAMETRIC AMPLIFIER TIME-DEPENDENT COUPLING BETWEEN ( ) OSCILLATORS 1 cos P a1 () t out a ( t ) a ( t) out 1 M = M + ε Ω t ωa MECHANICAL ANALOG ωb a ( t) Ω = ω + ω p 1 ωa ωb PUMP

46 WHY IS THE IMAGE PORT NEEDED? Manley-Rowe relations Δ N = Δ =ΔN P N S I Ω = ω + ω p 1 PUMP

47 NON-DEGENERATE PARAMETRIC PUMPING INTERNAL MODES resonant frequencies: ω1 and ω IN ω I ωs ω S ωi ω OUT ω I ω S ω S ωi ω Pump frequency Ω = ω + ω p 1

48 NON-DEGENERATE PARAMETRIC PUMPING INTERNAL MODES resonant frequencies: ω1 and ω IN ω I ωs ω S ωi ω OUT ω I ω S ω S ωi ω NOISELESS, UNITY PHOTON GAIN FREQUENCY CONVERSION! Pump frequency ω p 1 Ω = ω

49 GAIN-BANDWIDTH COMPROMISE 4 3 ( ) 1 Log1 S G ω B = 1 4κ aκ b G κa + κb when G 1 G ρ S I = G( ωs = ω1 ) = ρ = 1 ρ Z1Z ω ω ε ω S ω1 κ 1

50 4. Implementation of non-degenerate paramp with Josephson rg modulator

51 TOWARDS THE PUREST NON-LINEARITY: THE JOSEPHSON RING MODULATOR (Bergeal et al., 8, arxiv:85.345, to appear Nature Physics ) 4 junctions a rg threaded by flux 4 modes: H couplg ~ XYZ X Y Z X Y Z W The Z mode can be understood as providg an vertible mutual ductance between the X and Y mode

52 pump power P P c 1 bistability (self-oscillation with possible phases) PURE pump power P P c 1 ga maximum ga pot for parametric amplification pump detung ( ωp ωr) / Γ IMPURE chaos doma (high noise) 3 pump detung ( ωp ωr) / Γ

53 IMPLEMENTATION WITH JOSEPHSON RING MODULATOR Bergeal et al. arxiv:85.345v1 to appear Nature Physics Pump I p cosωt out a1 Signal (Z) Idler out a a1 ω a π = 1.6 GHz = 7GHz π (Y) Φ Ω = ω a + ω b Φ Φ ω b (X) a

54 IMPLEMENTATION WITH JOSEPHSON RING MODULATOR Pump I p cosωt out a1 Signal (Z) Idler out a a1 ω a π = 1.6 GHz = 7GHz π Φ ω b (Y) (X) Ω = ω a + ω b a G ( ω) = 1+ out a1 a1 G ω ( B /) G G 1 G 1 G a out a Qa Q b B= + ωa ωb 1 G / ρ G = 1+ ρ = 1 ρ 1 4 I p QQ a bpapb I

55 OPERATION OF JOSEPHSON PARAMETRIC CONVERTER out a 1 I p cosω p t (Z) ρ = I P / I c out a a 1 ω a =1.6 GHz (X) Φ ω b =7 GHz (Y) a Amplification Ω p = ω a + ω b Pure conversion Ω p = ω a - ω b out a1 a a1 out a G 1/ 1+ ρ = > 1 1 ρ out a1 a a1 out a r = 1 ρ 1+ ρ <1 1-port: amplification -port: up/down conversion power ga (amp. & conv ) photon ga mimal added noise : 1 ω 1-port: coolg -port: up/down conversion power ga conv. if ω out > ω no photon ga no added noise

56 CIRCUIT AT CHIP LEVEL Resonators: Frequencies: 1.6 GHz and 7. GHz test JJ Q's: 45 and 1 Bandwidths: 3.5 MHz and 6 MHz Junctions: I o = 3μA Input capacitances: SiOx

57 CHOSING WORKING POINT OF RING MODULATOR upward flux sweep color: phase of reflected signal (HF port) downward flux sweep Φ/ Φ

58 EXPERIMENTAL SETUP CHIP

59 AMPLIFICATION CHARACTERISTICS: GAIN vs FREQUENCY G 1 G 1 G G G G G 1 G 1

60 EXCELLENT AGREEMENT WITH PARAMP THEORY ( ) 1 a b BG = Γ +Γ 1/ MHz by extrapolation should get 1MHz with ga of db for 1GHz: OK for S-qubits

61 FREQUENCY CONVERSION up conversion down conversion G 1 G 1 G G G G G 1 G 1

62

63 DYNAMIC RANGE

64 MEASUREMENT OF SYSTEM NOISE WITH HOT NANOWIRE Self-calibrated measurement: V output Noise power T JPC pump -T N T

65 MEASUREMENT OF SYSTEM NOISE WITH HOT NANOWIRE Self-calibrated measurement: V output Noise power T JPC pump -T N T Nanowire as noise source: (J. Teufel s thesis, R. Schoelkopf, and D. Prober) Cu V N = hω hω coth kbt ( x, V ) L= 4 μm, t = nm, w = 8 nm (hot electron regime: nd self-calibration)

66 DIFFERENT REGIMES OF NOISE FOR NANOWIRE ( hω << k B T << ev ) HOT ELECTRON REGIME Stebach, Martis, Devoret, PRL 76, 386 (1996) Pothier, Gueron, Birge, Esteve, Devoret, PRL 79, 349 (1997) Spietz, Schoelkopf and Pari, APL 89, (6) John Teufel's thesis, Yale 8

67 DIFFERENT REGIMES OF NOISE FOR NANOWIRE ( hω << k B T << ev ) L e-e <L< L e-ph L=4 μm, t = nm, w = 8 nm HOT ELECTRON REGIME 8 Ω at 3K 5 Ω at 4K Stebach, Martis, Devoret, PRL 76, 386 (1996) Pothier, Gueron, Birge, Esteve, Devoret, PRL 79, 349 (1997) Spietz, Schoelkopf and Pari, APL 89, (6) John Teufel's thesis, Yale 8

68 NOISE POWER vs BIAS VOLTAGE 1x1-6 Noise power (uncalibrated) Voltage (μv)

69 NOISE POWER vs BIAS VOLTAGE Hot electron regime theory fits well: 1x1-6 Noise power (uncalibrated) Voltage (μv)

70 NOISE POWER vs BIAS VOLTAGE Other theories like shot noise regime expression do not fit: 1x1-6 Noise power (uncalibrated) Voltage (μv) CAN CONVERT VOLTAGE INTO EFFECTIVE TEMP ERATURE : kt eff = 3 8 ev

71 NOISE POWER vs EFFECTIVE TEMPERATURE 1x1-6 Noise Power (Uncalibrated, Watts) T eff (mk)

72 NOISE POWER vs EFFECTIVE TEMPERATURE 1x1-6 Noise Power (Uncalibrated, Watts) Quantum noise of load ( /) ω s T eff (mk)

73 NOISE POWER vs EFFECTIVE TEMPERATURE 1x1-6 Noise Power (Uncalibrated, Watts) Quantum noise of load ( /) ω s Noise added by system T eff (mk)

74 NOISE POWER vs EFFECTIVE TEMPERATURE 1x1-6 Noise Power (Uncalibrated, Watts) Quantum noise of load Noise added by system T eff (mk) system noise T N : 13mK

75 NOISE POWER vs EFFECTIVE TEMPERATURE 1x1-6 Noise Power (Uncalibrated, Watts) Quantum noise of load ( ω s /) IDEAL CASE T eff (mk) Quantum noise of idler load system noise T N : 13mK

76 NOISE POWER vs EFFECTIVE TEMPERATURE 1x1-6 Noise Power (Uncalibrated, Watts) Quantum noise of load ( ) / ω s -5 T eff (mk) 5 1 IDEAL CASE Quantum noise of idler load 15 system noise T N : 13mK quantum limited T N : 4mK

77 5. Squeezg

78 SIGNAL AND IDLER CO-AMPLIFICATION FOR NON-DEGENERATE PARAMETRIC AMPLIFIER a signal out a a out a idler sum of signal and idler is amplified

79 SIGNAL AND IDLER CO-AMPLIFICATION FOR NON-DEGENERATE PARAMETRIC AMPLIFIER a signal out a a out a idler sum of signal and idler is amplified (G 1/ ) difference of signal and idler is de-amplified (G -1/ ) total volume 4-d phase space is conserved

80 SIGNAL AND IDLER CO-AMPLIFICATION FOR NON-DEGENERATE PARAMETRIC AMPLIFIER signal a signal a out a idler out a idler

81 SQUEEZING OF QUANTUM FLUCT UATIONS FOR FOR NON-DEGENER ATE PARAM ETRIC AMP LIFIER signal port a vacuum state -MODE SQUEEZING signal port out a a amplification out a idler port b vacuum state of quantum noise idler port out b b out b see "Quantum Squeezg", Drummond and Ficek eds (Sprger 4)

82 SQUEEZING OF QUANTUM FLUCT UATIONS FOR FOR NON-DEGENER ATE PARAM ETRIC AMP LIFIER signal port a vacuum state signal port out a a amplification out a idler port b vacuum state of quantum noise idler port out b b out b see "Quantum Squeezg", Drummond and Ficek eds (Sprger 4)

83 SQUEEZING OF QUANTUM FLUCT UATIONS FOR FOR NON-DEGENER ATE PARAM ETRIC AMP LIFIER signal port a vacuum state signal port out a a out a amplification idler port b vacuum state of quantum noise idler port out b sub-zpm correlations b out b see "Quantum Squeezg", Drummond and Ficek eds (Sprger 4)

84 SQUEEZING OF QUANTUM FLUCT UATIONS FOR FOR NON-DEGENER ATE PARAM ETRIC AMP LIFIER signal port a vacuum state signal port out a thermal state a out a amplification idler port b vacuum state of quantum noise idler port out b sub-zpm correlations thermal state b out b see "Quantum Squeezg", Drummond and Ficek eds (Sprger 4)

85 SQUEEZING OF QUANTUM FLUCT UATIONS FOR FOR NON-DEGENER ATE PARAM ETRIC AMP LIFIER signal port a vacuum state signal port out a thermal state a amplification out a idler port b vacuum state of quantum noise idler port out b sub-zpm correlations thermal state b large ga limit: kt B eff ω = G out b see "Quantum Squeezg", Drummond and Ficek eds (Sprger 4)

86 TWO-MODE SQUEEZING OF QUANTUM FLUCT UATIONS signal noise G 1 (no put) (no put) G G 1 G idler noise

87 TWO-MODE SQUEEZING OF QUANTUM FLUCT UATIONS signal noise (no put) G G 1 G 1 G (no put) idler noise signal idler ω b ϕ ω + ω a b ω a ω a S.A. iϕ S + e I

88 TWO-MODE SQUEEZING OF QUANTUM FLUCT UATIONS signal noise (no put) G G 1 G 1 G (no put) idler noise signal idler ω b a ϕ ω + ω b ω a ω a S.A. iϕ S + e I 1. Magnitude (normalized) Data S ϕ ( radians) 1 1

89 TWO-MODE SQUEEZING OF QUANTUM FLUCT UATIONS signal noise (no put) G 1 G G G 1 S + I = G kbtn (no put) idler noise iϕ S + e I signal idler ω b a ϕ ω + ω b ω a ω a S.A. iϕ S + e I 1. Power (db, normalized) ( db) Magnitude (normalized) Data S db squeezg 6 db ( S + I ) = G hω From noise measurement G = 3dB

90 6. Lk between Josephson paramps and μw-squids (with Archana Kamal and John Clarke)

91 PARAMP APPROACH TO SQUIDS IN ω J ωs ω S 4 INTERNAL MODES ωj ω ω ω OUT Ω = p ω J Ω = ω p1 J ω

92 Josephson paramps are predictible: experimental characteristics data agree very well with theoretical model, even for large ga. Their noise performance can be controlled. System noise performance ~ times better than with HEMT amplifier only Evidence for -mode squeezg of quantum fluctuations, frequency conversion and dynamic coolg Next: CONCLUSIONS AND PERPECTIVES - Increase bandwidth, tailor resonant frequency and produce devices for qubit readout cqed experiments - Increase two-mode squeezg for multi-photon terference - SQUID-paramp hybrid?