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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 – MQC

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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

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Quantum Mechanics (QM) Classical Mechanics (CM) Superposition Principle Macrorealism A. Leggett : Can we have a non classical behavior in a macroscopic system? MQC = Macroscopic Quantum Coherence Einstein, Podolski, Rosen : The description of (microscopic) reality given by the quantum wave function is not complete J. Bell : We can imagine a two particle experiment giving different results for CM (locality) or QM (non locality) A. Aspect : Bell experiment with two polarized photons. Violation of Bell inequalities. Non locality.

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A. J. Leggett, 1985, first proposal of MQC

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The double well potential: Leggett 1985: propose a device having a double well potential (a SQUID) to create a double well potential

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rf SQUID states: L & R U( ) L> R> ESEAESEA I

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MQC (Rabi Oscillations) : QM vs. MR : P(L,t L, t=0) cos 2 t where = tunnelling frequency between wells P(t) t 1 1/2 0

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Non Classical Behavior Violation of Bell Inequalities Superposition principle verified Violation of Macrorealism Violation of NIM (Non Invasive Measurement) Macroscopic System N (number of interacting particles) >> 1. S (Action) >> h/4. The measuring apparatus of microscopic objects. Any system isolated from the external world for a time long with respect to the duration of the observation.

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Definitions (G.C. Ghirardi, Found. Phys. Lett. 1994) Macrorealism (MR): If a macroscopic system under certain conditions is, whenever observed, found to be in one of two or more macroscopically distinguishable states, then we can assign to it at nearly all times, i.e. even when it is not observed, the property of actually being in a particular one of these states. Non Invasive Measurement (NIM): For such a system it is, in principle, possible to observe which of the various possible macrostates it is in, without affecting its subsequent behavior, at least as regards motion between macrostates.

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The goal of the experiment is to realize a set of measurements to verify if the formalism of Quantum Mechanics and related predictions are still valid for a macroscopic system Conceptual Scheme Magnetic flux Superconducting Switch Voltmeter Two level system Analyzer Counter S A C Polarized Photons Polarizer Counter MQC – Roma - INFN

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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 dellAquila 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

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Organizzazione: Roma – CNR, LAquila 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

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N : 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(-T c /T)] The system Hamiltonian is non linear. The effect can be seen in reasonable short times (ns s). L (superconducting) + Josephson Junction = SQUID I MQC can be realized with a SQUID

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Il potenziale dello SQUID (rf-dc-jj...) La pendenza media può essere variata dallesterno (corrente-flusso) Varia laltezza della barriera di potenziale Variano le frequenze di tunneling Variano le distanze fra i vari livelli energetici E 1 > E 2 > E 3 analogamente variano le risonanze con i livelli energetici delle buche adiacenti

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macroscopic system: rf-SQUID energy eigenstates: t symmetric and antisymmetric superposition of states superconducting ring with one JJ described by a macroscopic degree of freedom, the magnetic flux threading the ring dynamics governed by a double- well potential (under proper bias) U( ) L> R>

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Preparation of the flux state (L) Flux Measurement after t Repeat for differents t Evaluate the Probability P(L,L) I- Detection of Rabi oscillations Plan of measurements (3 tests)

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State preparation Non Invasive Measurement State Measurement II- Test of (classical) Non Invasivity

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State preparation. (Left State) Non Invasive Measurement (Keep only LEFT results) State Measurement: Macroscopic Realism or QM ? tmtm tmtm ? III- Test of Macrorealism vs. QM

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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 P(t) t 1 1/2 0

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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 m 3 (34 dB attenuation of Earth magnetic field within 1 dm 3 ) Magnetically levitated turbo pump Vibration Isolation platform, frequency cut ~1 Hz. Sample immersed in the liquid 3 He- 4 He mixture. Rome group Leiden cryogenics Low Temperature: 3 He- 4 He dilution refrigerator

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SQUID Switch SQUID Amplifier SQUID rf rf bias dc bias laser V out ( ) Scheme of the experimental SQUID system

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Chip for the MQC experiment dc-SQUID amplifier readout hysteretic dc-SQUID tunable rf-SQUID coils 100 m

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A two-hole hysteretic dc-SQUID Nb/AlOx/Nb trilayer L=5pH hole size: 10 m I 0 = 4-25 A JJ size: 3 m Josephson junction coil for magnetic flux coupling and tune current 5 m wire top contact bottom contact SQUID holes

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We need a very precise starting time for the free evolution of the SQUID flux oscillations Why a Laser Switch ? laser off laser on I=I 0 I=0 after 10ns U( )

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Readout scheme to test the laser switch Laser P(t) I b (t) V(t) t T=4.2 K V(t) Laser P(t) I b (t) 2 m

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Measurements of the voltage pulse from the switch Data R(t)=a t V(t)=I 0 a t exp(-a t 2 / 2L) 500 MHz bandwidth V (mV) MHz bandwidth amplifier V(mV) Time ( s)Time (ns) V(t)dt=LI 0 is independent from the amplifier bandwidth

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Lo SQUID di lettura per effettuare misure non invasive (un dc SQUID)

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Readout with a hysteretic dc-SQUID R L I c * > I bias no transition dc SQUID remains at V=0 I c * < I bias transition to V 0 V I IcIc I bias Ic*Ic* V I IcIc Ic*Ic* V I

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Utilizzo di un dc-SQUID per la misura non invasiva dello SQUID rf = R V out = 0 = L V out 0 Il dc SQUID viene acceso da un impulso di corrente, che lo mantiene nello stato superconduttore, V=0 NIM: Non Invasive Measurement Misura Invasiva: si scarta R v out IbIb L IbIb

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Sensibilità: larghezza della transizione V=0 V 0 Switch probability of hysteretic dc-SQUID as a function of applied magnetic flux and temperature

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Detection efficiency: prediction: 98% measured: 98% P m current bias of hysteretic SQUID voltage output of hysteretic SQUID voltage output of SQUID magnetometer optimal bias point

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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.

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Diminuendo laltezza della barriera si provoca lescape 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 2 c Misure di Energy Level Quantization per valutare la dissipazione intrinseca del sistema

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e Escape rate for a Josephson junction T= 20 mK - R 1 M Escape rate for an rf SQUID T=35mK - R 4 M (s -1 ) Experimental results (C. Cosmelli et al. Phys. Rev. Lett. 1999) ( C. Cosmelli et al. Phys. Rev. 1998)

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Energy level quantization in thermal regime fast sweeping of the current, non-stationary regime, T > T crossover T=1.3 K (IC-Napoli)

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Misura delle oscillazioni di Rabi in un sistema macroscopico (un dc SQUID non un rf SQUID!)

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Physical implementation – Measurement set up T=300K

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Test with continuous microwaves - I Switching probability P at different x : - switching curve - peaks For each flux: sequence of current pulses For each pulse: voltage read-out (0 or 2.7mV) Continuous microwaves at fixed frequency f Different fluxes x

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Test with continuos microwaves - II To find the peaks positions: - Hamiltonian Eigenenergies E 0, E 1, E 2,... - Fluxes to have f= (E n -E 0 )h Microwaves can excite the system when f=(E n -E 0 )h Peaks at the expected positions f = GHz I pulse = 5.5 A t pulse = 50 ns I 0max = 19 A C tot = 1.1 pF L = 12 pH T = 60 mK Experimental values

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Test with short pulses of microwaves Flux fixed on the second peak at x = 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. wave pulse

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Results: Rabi Oscillations on a Macroscopic System frequency of oscillations =7,4 MHz Decoherence time = 150 ns T c (thermal/quantum regime) 100 mK The plot represents the probability P[ |1>,t ; |0>, 0] as a function of the microwave pulse duration t f = GHz hf/K B =720 mK x = I pulse = 5.5 A t pulse = 50 ns I 0max = 19 A C tot = 1.1 pF L = 12 pH T = 60 mK System parameters

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wave power dependence Continuous microwaves, different powers Range to observe peaks: ~ 9.5 dBm – 10.5 dBm

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World state of art – observation of coherence on macroscopic systems (SQUIDs) Group System Indirect obs. (level rep.) Direct obs. Rabi osc. Stony Brook USA rfSQUID 1JJ x Delft, NL SQUID 3JJ xx Rome, Italy dcSQUID 2JJ x Work in progress: Berkeley (USA), IBM (USA)

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(K) energy |i |0 |1 J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo and J. E. Lukens Nature 2000 tunable rf-SQUID superposition of two excited states |0> and |1> look for interwell transitions caused by photon absorption spectroscopic measurement

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C. van der Wal, J.E. Moij et al., Science 99 3 junctions, one with different E J double well potential Superconducting vortex qubit read with surrounding underdamped dc-SQUID

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peak and dip under -wave resonance between photon and energy spacing between lowest quantum states level repulsion

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Sviluppi futuri: SQC Superconducting Quantum Computing SQC è attualmente finanziato in gruppo V – end 2004

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Carlo Cosmelli, Roma Classical computer bit 1 bit two states 0 1 :It isdeterministicreading a bitgives always the value of itsstate 0 or 1 Theoutputis 0 or 1 :a : 2 qubit It isprobabilisticreading gives the value |0>with probability |1>with probability 2 Theoutputis 0 or 1 Quantum computing vs. Classical Computing Quantum computer qubit |0> 1 qubit |0> + |1> states

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Factorization times: QC power 1977 M. Gardner propose the factorization of a 129 bit number1977 M. Gardner propose the factorization of a 129 bit number 1994 The number is factorized: 1000 Workstations – 8 months1994 The number is factorized: 1000 Workstations – 8 months Classical computer Quantum Computer

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A hysteretic dc SQUID as a qubit system Potential Tunable system Artificial atom - Qubit states: |E 0 >, |E 1 > - Manipulation: Rabi oscillations - Read-out: current pulse to reduce U in order to have escape from E 1 and not from E 0 i 0 : single junction critical current

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A double rf SQUID as a qubit system Potential Tunable system Pseudo-spin ½ system - Qubit states: | L >, | R > - Manipulation: Rabi oscillations, external fluxes variations - Read-out: SQUID magnetometer or flux comparator

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Quantum Information Technology: Public Founding, next 5 years Japan20 M/year Japan20 M/year Europe (EC) 7 M/year + Single States Europe (EC) 7 M/year + Single States USA 6 M/year + Universities USA 6 M/year + Universities Includes all QIT (Solid State, Photons, Quantum Dots, Atoms, Semiconductors, Molecules,....) for experimental and theoretical research.

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