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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 –

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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 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. A. Leggett : Can we have a non classical behavior in a macroscopic system? MQC = Macroscopic Quantum Coherence

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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 I U(f) L> R> f ES EA

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**MQC (Rabi Oscillations) : QM vs. MR :**

P(L,tL, t=0) cos2 t where = tunnelling frequency between wells P(t) t 1 1/2

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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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**MQC – Roma - INFN Conceptual Scheme S A C**

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 Two level system Analyzer Counter S A C Polarized Photons Polarizer Counter Magnetic flux Superconducting Switch Voltmeter

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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 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

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**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

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**MQC can be realized with a SQUID**

L (superconducting) Josephson Junction = SQUID I N : Cooper pairs; I 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).

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**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

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**t symmetric and antisymmetric superposition of states**

macroscopic system: rf-SQUID 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(f) L> R> f energy eigenstates: t symmetric and antisymmetric superposition of states

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**Plan of measurements (3 tests)**

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

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**II- Test of (classical) Non Invasivity**

State preparation Non Invasive Measurement State Measurement

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**III- Test of Macrorealism vs. QM**

State preparation. (Left State) Non Invasive Measurement (Keep only LEFT results) State Measurement: Macroscopic Realism or QM ? tm tm ?

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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)] P(t) t 1 1/2 low temperature :T< 20mK low dissipation : R > 1 M

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**Low Temperature: 3He-4He dilution refrigerator**

Rome group Leiden cryogenics 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.

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**Scheme of the experimental SQUID system**

dc bias laser SQUID Switch Vout(f) SQUID rf rf bias SQUID Amplifier

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**Chip for the MQC experiment**

dc-SQUID amplifier coils tunable rf-SQUID readout hysteretic dc-SQUID 100m

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**A two-hole hysteretic dc-SQUID**

top contact bottom contact SQUID holes coil for magnetic flux coupling and tune current SQUID holes 5 mm wire Nb/AlOx/Nb trilayer L=5pH hole size: 10 mm I0 = mA JJ size: 3 mm Josephson junction

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Why a Laser Switch ? We need a very precise starting time for the free evolution of the SQUID flux oscillations laser off U() I=I0 laser on U() I=0 after 10ns

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**Readout scheme to test the laser switch**

T=4.2 K V(t) Laser P(t) Ib(t) 2 m Laser P(t) Ib(t) V(t) t

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**Measurements of the voltage pulse from the switch**

1MHz bandwidth amplifier 500 MHz bandwidth -40 -20 20 40 60 -3 -2 -1 1 0.00 Data -0.02 -0.04 V(mV) V (mV) -0.06 -0.08 -0.10 0.0 0.5 1.0 1.5 2.0 Time (ms) Time (ns) R(t)=a t V(t)=I a t exp(-a t 2 / 2L) V(t)dt=LI0 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**

FR FL V I V I V I Ic* Ic Ic Ibias Ibias Ic* Ic*> Ibias no transition dc SQUID remains at V=0 Ic* < Ibias transition to V 0

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**Utilizzo di un dc-SQUID per la misura non invasiva dello SQUID rf**

FR vout Ib FL vout Ib 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

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**Sensibilità: larghezza della transizione V=0 V0**

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%**

current bias of hysteretic SQUID P voltage output of hysteretic SQUID voltage output of SQUID magnetometer F (mF0) 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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**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

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**Experimental results e0 Escape rate for a Josephson junction**

105 103 101 10-1 .964 .968 .972 .976 I/Ic 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 e0 (C. Cosmelli et al. Phys. Rev. Lett. 1999)

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**Energy level quantization in thermal regime**

fast sweeping of the current, non-stationary regime, T > Tcrossover 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**

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

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**Test with continuos microwaves - II**

To find the peaks positions: Hamiltonian Eigenenergies E0, E1, E2, ... Fluxes to have f= (En-E0)h Microwaves can excite the system when f=(En-E0)h Peaks at the expected positions f = GHz Ipulse = 5.5 mA Dtpulse = 50 ns I0max = 19 mA Ctot = 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 Fx = 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. wave pulse

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**Results: Rabi Oscillations on a Macroscopic System**

The plot represents the probability P[ |1>,t ; |0>, 0] as a function of the microwave pulse duration Dt f = GHz hf/KB=720 mK Fx = F0 Ipulse = 5.5 mA Dtpulse = 50 ns I0max = 19 mA Ctot = 1.1 pF L = 12 pH T = 60 mK System parameters frequency of oscillations =7,4 MHz Decoherence time = 150 ns Tc (thermal/quantum regime) 100 mK

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**m wave power dependence**

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

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**Work in progress: Berkeley (USA), IBM (USA)**

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 Rome, Italy dcSQUID 2JJ Work in progress: Berkeley (USA), IBM (USA)

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

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**Superconducting vortex qubit**

C. van der Wal, J.E. Moij et al., Science 99 3 junctions, one with different EJ double well potential 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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**The output is 0 or 1 The output is 0 or 1 Quantum computing vs.**

Classical Computing Classical computer { bit } 1 bit two states 1 Quantum computer { qubit } |0> 1 qubit a |0> + b |1> states It is deterministic reading a bit gives always the value of its state 0 or : qubit It is probabilistic reading gives the value |0> with probability a |1> b : a : 2 2 The output is 0 or The output is 0 or Carlo Cosmelli, Roma

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**Factorization times: QC power**

1977 M. Gardner propose the factorization of a 129 bit number 1994 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 i0 : single junction critical current Tunable 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

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**A double rf SQUID as a qubit system**

Potential Tunable 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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**Quantum Information Technology: Public Founding, next 5 years**

Japan 20 M€/year Europe (EC) 7 M€/year + Single States 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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