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MQC. Macroscopic Quantum Coherence. Carlo Cosmelli, G. Diambrini Palazzi Dipartimento di Fisica, Universita`di Roma “La Sapienza”. Istituto Nazionale di Fisica Nucleare Commissione Nazionale II- Relazione Finale – 19.11.2003. Sommario. Introduzione storica, la proposta di A. Leggett
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MQC Macroscopic Quantum Coherence Carlo Cosmelli, G. Diambrini Palazzi Dipartimento di Fisica, Universita`di Roma “La Sapienza” Istituto Nazionale di Fisica Nucleare Commissione Nazionale II- Relazione Finale – 19.11.2003
Sommario • Introduzione storica, la proposta di A. Leggett • MQC con rf SQUID, MQC a Roma • Misure e risultati intermedi: • Il dispositivo • (Il Laser switch) • Misure non invasive • Misure di dissipazione quantistica • Misura delle oscillazioni di Rabi: MQC con un dc SQUID • Sviluppi a Roma e nel mondo: la computazione quantistica
Quantum Mechanics (QM) Classical Mechanics (CM) Superposition Principle Macrorealism 1935 - Einstein, Podolski, Rosen : The description of (microscopic) reality given by the quantum wave function is not complete 1964 - J. Bell : We can imagine a two particle experiment giving different results for CM (locality) or QM (non locality). 1972 - A. Aspect : Bell experiment with two polarized photons. Violation of Bell inequalities. Non locality. 1985 - A. Leggett : Can we have a non classical behavior in a macroscopic system? MQC = Macroscopic Quantum Coherence
The double well potential: Leggett 1985: propose a device having a double well potential (a SQUID) to create a double well potential
U(f) L> R> f I rf SQUID states: L & R ES EA
P(t) 1 1/2 0 t MQC (Rabi Oscillations) :QM vs. MR : P(L,tL, t=0) cos2 t where = tunnelling frequency between wells
Il gruppo MQC: (in giallo i membri temporanei) • Università La Sapienza • G. Diambrini Palazzi, C. Cosmelli, F. Chiarello, D. Fargion, INFN Roma • Istituto Fotonica e Nanotecnologie – CNR, Roma • M.G. Castellano, R. Leoni, G. Torrioli, INFN Roma • Università dell’Aquila • P. Carelli, G. Rotoli,INFN G. C. Sasso/Tor Vergata • Università di Tor Vergata • M. Cirillo, INFN Tor Vergata • Istituto di Cibernetica – CNR- Napoli • R. Cristiano, G. Frunzio, B.Ruggiero, P. Silvestrini, INFN Napoli • Istituto Regina Elena –Centro Ricerche • L. Chiatti • 9 Laureandi, 2 Dottorandi
Organizzazione: • Roma – CNR, L’Aquila • Progettazione dispositivi superconduttori • Realizzazione dispositivi • Test preliminari a T= 4.2 K • Roma – La Sapienza • Simulazioni • Test a rf a T=4.2 K • Test a T<100mK • Analisi Risultati
I L (superconducting) + Josephson Junction = SQUID MQC can be realized with a SQUID • N : 1010 Cooper pairs; I 1-10 A • The system dynamics can be controlled and measured in the classical regime ( J. Clarke, 1987). • The intrinsic dissipation can be made negligible [ exp(-Tc/T)] • The system Hamiltonian is non linear. • The effect can be seen in reasonable short times (nss).
Il potenziale dello SQUID (rf-dc-jj...) • La pendenza media può essere variata dall’esterno (corrente-flusso) • Varia l’altezza della barriera di potenziale • Variano le frequenze di tunneling • Variano le distanze fra i vari livelli energetici E1> E2> E3 analogamente variano le risonanze con i livelli energetici delle buche adiacenti
P(t) 1 1/2 0 t Experimental Requirements • Suppose we want to observe oscillations from one well to the other with tunneling frequency • The tunneling probability is exponentially depressed by dissipation (Caldeira, Leggett, Garg) • P(t) =1/2[1+cos (t) exp (- t)] low temperature :T< 20mK low dissipation : R > 1 M
Rome group Leiden cryogenics Low Temperature: 3He-4He dilution refrigerator • T=9 mK, power= 200 W at 120 mK • 3 -metal shields (> 40 dB between dc and 100 Hz) • 2 Al shields (> 90 dB at 1 MHz) • Set of Helmoltz coils 1.5x1.5x1.5 m3 (34 dB attenuation of Earth magnetic field within 1 dm3) • Magnetically levitated turbo pump • Vibration Isolation platform, frequency cut ~1 Hz. • Sample immersed in the liquid 3He-4He mixture.
Scheme of the experimental SQUID system dc bias laser SQUID Switch Vout(f) SQUID rf rf bias SQUID Amplifier
dc-SQUID amplifier coils tunable rf-SQUID readout hysteretic dc-SQUID Chip for the MQC experiment 100m
Lo SQUID di letturaper effettuare misure non invasive (un dc SQUID)
vout vout Ib Ib FR FL Utilizzo di un dc-SQUID per la misura non invasiva dello SQUID rf Il dc SQUID viene “acceso” da un impulso di corrente, che lo mantiene nello stato superconduttore, V=0 = R Vout= 0 = L Vout 0 NIM: Non Invasive Measurement Misura Invasiva: si scarta
Sensibilità: larghezza della transizione V=0 V0 Switch probability of hysteretic dc-SQUID as a function of applied magnetic flux and temperature
Detection efficiency:prediction: 98%measured: 98% current bias of hysteretic SQUID P voltage output of hysteretic SQUID voltage output of SQUID magnetometer F (mF0) optimal bias point
The Problem of Dissipation • Shield all cables from high temperature signals • Shield from external e.m. fields • Shield from mechanical vibrations • Leave only intrinsic dissipation • Measure overall dissipation.
Misure di Energy Level Quantization per valutare la dissipazione intrinseca del sistema Diminuendo l’altezza della barriera si provoca l’escape per tunneling dei vari livelli energetici: si misura =1/ in funzione dello sbilanciamento Dalla forma di si calcola il valore della dissipazione effettiva del sistema 2c
(s-1) 105 103 101 10-1 .964 .968 .972 .976 I/Ic Experimental results Escape rate for a Josephson junction T= 20 mK - R 1 M (C. Cosmelli et al. Phys. Rev. 1998) (s-1) Escape rate for an rf SQUID T=35mK - R 4 M 103 101 10-1 -.48 -.47 -.46 (C. Cosmelli et al. Phys. Rev. Lett. 1999) e0
Energy level quantization in thermal regime fast sweeping of the current, non-stationary regime, T > Tcrossover T=1.3 K (IC-Napoli)
Misura delle oscillazioni di Rabiin un sistema macroscopico(un dc SQUID non un rf SQUID!)
Continuous microwaves at fixed frequency f • Different fluxes Fx • For each flux: sequence of current pulses • For each pulse: voltage read-out (0 or 2.7mV) • Switching probability P at different Fx: • switching curve • peaks Test with continuous microwaves - I
Microwaves can excite the system when f=(En-E0)h • To find the peaks positions: • Hamiltonian Eigenenergies E0, E1, E2, ... • Fluxes to have f= (En-E0)h Peaks at the expected positions Experimental values f = 14.999 GHz Ipulse = 5.5 mA Dtpulse = 50 ns I0max = 19 mA Ctot = 1.1 pF L = 12 pH T = 60 mK Test with continuos microwaves - II
wave pulse Test with short pulses of microwaves • Flux fixed on the second peak at Fx = 0.405 F0 • A short (100 ns – 500 ns) pulse of microwaves is applied to the dc SQUID • A reading current pulse of proper shape is send to the dc SQUID • The voltage across the SQUID (0 or 2,7 mV) is read at a proper time.
The plot represents the probability P[ |1>,t ; |0>, 0] as a function of the microwave pulse duration Dt Systemparameters f = 14.999 GHz hf/KB=720 mK Fx = 0.405 F0 Ipulse = 5.5 mA Dtpulse = 50 ns I0max = 19 mA Ctot = 1.1 pF L = 12 pH T = 60 mK Results: Rabi Oscillations on a Macroscopic System • frequency of oscillations =7,4 MHz • Decoherence time = 150 ns • Tc (thermal/quantum regime) 100 mK
World state of art – observation of coherence on macroscopic systems (SQUIDs) Work in progress: Berkeley (USA), IBM (USA)
peak and dip under -wave resonance between photon and energy spacing between lowest quantum states level repulsion
Sviluppi futuri: SQC Superconducting Quantum Computing SQC è attualmente finanziato in gruppo V – end 2004
Quantum computing vs. Classical Computing Quantum computing vs. Classical Computing bit qubit bit qubit { } { } { } { } Classical computer Quantum computer Classical computer Quantum computer º º º º 0 |0> 1 bit two states 1 qubit |0> + |1> a b 1 ¥ ¥ states states |1> It is probabilistic reading It is deterministic reading qubit gives the value a bit gives always the value of its state |0> with probability a 0 or 1 |1> with probability b The output is 0 or 1 : a : : 2 2 The output is 0 or 1 Carlo Cosmelli, Roma
Quantum Computer Classical computer Factorization times: QC power • 1977 M. Gardner propose the factorization of a 129 bit number • 1994 The number is factorized: 1000 Workstations – 8 months
Potential i0 : single junction critical current Tunable system A hysteretic dc SQUID as a qubit system “Artificial atom” - Qubit states: |E0>, |E1> - Manipulation: Rabi oscillations - Read-out: current pulse to reduce DU in order to have escape from E1 and not from E0
Potential Tunable system A double rf SQUID as a qubit system “Pseudo-spin ½ system” - Qubit states: |FL>, |FR> - Manipulation: Rabi oscillations, external fluxes variations - Read-out: SQUID magnetometer or flux comparator
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