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

MQC

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

1985 - A. Leggett : Can we have a non classical behavior in a macroscopic system? MQC = Macroscopic Quantum Coherence

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.

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

The double well potential:

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

rf SQUID states: L & R

U()

L> R>

[ ]22

E2

1 pASRLAS

τω±

ω=ψ±ψ=ψ

hh,, ;

[ ]ASASRL2

1,,, ψ±ψ=ψES

EA

( ) ( ) ( )[ ]tEE121

2

1As2

1LP AsAS −+=ψ+ψ?ψ+ψ= cos**

( ) ( ) ( )[ ]tEE121

2

1As2

1RP AsAS −−=ψ−ψ?ψ−ψ= cos**

2t

2t

2

2

τ

τ

ω

ω

sin

cos

I

MQC (Rabi Oscillations) :QM vs. MR :

P(L,tL, t=0) cos2 ωτt

where ωτ= tunnelling frequency between

wells P(t)

t

1

1/2

0

tP LL♦

t0

1

0.5

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

• 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).

L (superconducting) + Josephson Junction = SQUID

I

MQC can be realized with a SQUID

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

Experimental Requirements•Suppose we want to observe oscillations

from one well to the other with tunneling frequency ω

•The tunneling probability is exponentially depressed by dissipation (Caldeira, Leggett, Garg)

•P(t) =1/2[1+cos (ωt) exp (- t)]

low temperature :T< 20mK

low dissipation : R > 1 M

8 2

20

R

Tk

hφ =P(t)

t

1

1/2

0

• 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.

Rome groupLeiden cryogenics

Low Temperature: 3He-4He dilution refrigerator

SQUID Switch

SQUID Amplifier

SQUID rf

rf bias

dc bias

laser

Vout()

Scheme of the experimental SQUID system

Chip for the MQC experiment

dc-SQUIDamplifier

readouthystereticdc-SQUID

tunablerf-SQUID

coils

100m

Lo SQUID di lettura

per effettuare misure non

invasive

(un dc SQUID)

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

= R Vout= 0 = L Vout 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

voutIb

L

voutIb

Sensibilità: larghezza della transizione V=0 V0

0.290 0.295 0.300

0.0

0.2

0.4

0.6

0.8

1.0

18 mK 73 mK 150 mK 283 mK 373 mK 535 mK 626 mK

P switch

ext (

0)

Switch probability of hysteretic dc-SQUID as a function of applied magnetic flux and temperature

Detection efficiency:

prediction: 98%

measured: 98%

82 84 86 88 90 92 94 96 98 100 1020.0

0.2

0.4

0.6

0.8

1.0(a)

(b)

U()f rf

U()f rf

L

R

0 20 40 60 80 100 120 140 160 180 200

t (ms)

P

m0

current bias of hysteretic SQUID

voltage output of hysteretic SQUID

voltage output of SQUID magnetometer

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.

U(x )

Diminuendo l’altezza della barriera si provoca l’escape per tunneling dei vari livelli energetici: si misura =1/τ in funzione dello sbilanciamento

Dalla forma di si calcola il valore della dissipazione effettiva del sistema

2c

Misure di Energy Level Quantization per valutare la dissipazione intrinseca del sistema

(s-

1)105

103

101

10-1

.964 .968 .972 .976 I/Ic

e0

-.46-.47-.48

Escape rate for a Josephson junction

T= 20 mK - R 1 M

Escape rate for an rf SQUID

T=35mK - R 4 M

103

101

10-1

(s-1)

Experimental results

(C. Cosmelli et al. Phys. Rev. Lett. 1999)

(C. Cosmelli et al. Phys. Rev. 1998)

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 Rabi

in un sistema macroscopico(un dc SQUID non un rf SQUID!)

Test with continuous microwaves - I

0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46

0.0

0.2

0.4

0.6

0.8

1.0

0.405 0

0.391 0P

Φx (Φ

0)

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)

Ib

V

Ib

x

V • Continuous microwaves at fixed frequency f• Different fluxes x

Test with continuos microwaves - II

E0

E1

E2

U()

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

x0 ()

f (GHz)

( E- E)/ h1 0

( E- E)/ h20

0.391 Φ00.405 Φ0

Microwaves

Peaks at the expected positions

f = 14.999 GHzIpulse = 5.5 Atpulse = 50 nsI0max = 19 ACtot = 1.1 pFL = 12 pHT = 60 mK

Experimental values

Test with short pulses of microwaves

• Flux fixed on the second peak at x = 0.405 0

• 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.

rfpulse

Ib

V

t t

1

0

1

0

wave pulse

Results: Rabi Oscillations on a Macroscopic Results: Rabi Oscillations on a Macroscopic SystemSystem

• frequency of oscillations =7,4 MHz

• Decoherence time τ = 150 ns

• Tc (thermal/quantum regime) 100 mK

0.1 0.2 0.3 0.4 0.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

P

t (s)

The plot represents the probability P[ |1>,t ; |0>, 0] as a function of the microwave pulse duration t

f = 14.999 GHz

hf/KB=720 mK

x = 0.405 0

Ipulse = 5.5 A

tpulse = 50 ns

I0max = 19 A

Ctot = 1.1 pF

L = 12 pHT = 60 mK

System parameters

World state of art – observation of coherence on macroscopic systems (SQUIDs)

Group System

Indirect obs.

(level rep.)

Direct obs. Rabi osc.

Stony BrookUSA

rfSQUID 1JJ xDelft, NL SQUID 3JJ x xRome, Italy

dcSQUID2JJ x

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

Carlo Cosmelli, Roma

ClassicalClassicalcomputer computer bitbit

1 bit two states

0

1

:It is deterministicreadinga bitgives always the value of its state

0 or 1

Theoutput is

0 or 1

: a :

2

qubitIt is probabilisticreading

gives the value

|0> with probability

|1> with probability 2

Theoutput is

0 or 1

Quantum computing vs.Quantum computing vs.ClassicalClassicalComputingComputing

Quantum computer Quantum computer qubitqubit|0>

1 qubit |0> + |1>

|1> states states

Carlo Cosmelli, Roma

What kind of problems can be solved only What kind of problems can be solved only by a QC?by a QC?

The complexity of a problem can beThe complexity of a problem can be: :

(N=number of digit in input)(N=number of digit in input)

•• Polynomial P: op Polynomial P: op ∝∝ NNaa

•• NonNon-- Polynomial NP: op Polynomial NP: op ∝∝ exp(N)exp(N)

Ex: f actorization of an integer in prime f actors is NP Ex: f actorization of an integer in prime f actors is NP We know how to solve the problem, but we do not have We know how to solve the problem, but we do not have the time!the time!

The time is proportionalThe time is proportional

to the nto the noo of operationsof operations0 5 10 15 20 25 30

100

101

102

103

104

105

106

Time - n

o of operations

number of digits N

exp(N) N2

Factorization times: QC powerFactorization times: QC power

•1977 M. Gardner propose the factorization of a 129 bit 1977 M. Gardner propose the factorization of a 129 bit number number

•1994 The number is factorized: 1000 Workstations – 8 1994 The number is factorized: 1000 Workstations – 8

monthsmonths

2000 2005 2010 2015 2020 2025 203010-3

100

103

106

109

1012

1015

miniaturization limit

2048 bits

1024 bits

512 bit - 4 days

τ( )years

Year of fabrication

Classical Classical computercomputer

100 1000 1000010-1

100

101

102

103

2048 bits

1024 bits

4096 bits

512 bits

Factorization timesQuantum Computer [clock frequency: 100MHz]

τ( )minutes

Number of bits

Quantum Quantum ComputerComputer

A hysteretic dc SQUID as a qubit system

0cosBbBUII≅−−Potential

()()()()0000,12cos/,,,xxbxbxIiUIEIπΦ≅ΦΦΔΦΦTunable system

“Artificial atom”

- Qubit states: |E0>, |E1> - Manipulation: Rabi oscillations- Read-out: current pulse to reduce U in order to have escape from E1 and not from E0

E0

E1

U()

=E-E10

U

Ib

x

V=d/dtB

Microwaves

0/2/2Bhee……hi0 : single junction critical current

A double rf SQUID as a qubit system

()()201cos/2BBxUIL≅−ΦΦΦ+Φ−ΦPotential

()()()()0002cos/,,,xdcxdcxxdcxxdcIiUπεΦ≅ΦΦΔΦΦΔΦΦTunable system

“Pseudo-spin ½ system”- Qubit states: |L>, |R> - Manipulation: Rabi oscillations, external fluxes variations- Read-out: SQUID magnetometer or flux comparatorε

U

|>ΦL |>ΦR

Φ

U()Φ

x

Φdcx ΦΦdc

Microwaves

Flux read-outSQUI D

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