macroscopic quantum coherence
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Macroscopic Quantum Coherence
Carlo Cosmelli, G. Diambrini Palazzi Dipartimento di Fisica, Universita`di Roma “La Sapienza”
Istituto Nazionale di Fisica NucleareCommissione 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 complete1964 - 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>
[ ] 22E21 p
ASRLASτω±ω=ψ±ψ=ψ hh
,, ;
[ ]ASASRL 21
,,, ψ±ψ=ψESEA
( ) ( ) ( )[ ]tEE121
21
As21
LP AsAS −+=ψ+ψ?ψ+ψ= cos**
( ) ( ) ( )[ ]tEE121
21
As21
RP 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 ωτtwhere ωτ= tunnelling frequency between wells P(t)
t
1
1/2
0
tP LL♦
τ0
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< 20mKlow dissipation : R > 1 M
8 2
20
RTk
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 biaslaser
Vout()
Scheme of the experimental SQUID system
Chip for the MQC experiment
dc-SQUIDamplifier
readouthystereticdc-SQUID
tunablerf-SQUID
coils
100m
Lo SQUID di letturaper 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
exτ (
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 SQUIDT=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 (Φ0)
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)/ h2 0
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
τ τ
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 0.50.00.10.20.30.40.50.60.70.80.91.0
P
τ (s)
The plot represents the probability P[ |1>,t ; |0>, 0] as a function of the microwave pulse duration t
f = 14.999 GHzhf/KB=720 mKx = 0.405 0
Ipulse = 5.5 Atpulse = 50 nsI0max = 19 ACtot = 1.1 pFL = 12 pHT = 60 mK
System parameters
World state of art – observation of coherence on macroscopic systems (SQUIDs)
Group SystemIndirect
obs.(level rep.)
Direct obs. Rabi osc.
Stony BrookUSA rfSQUID 1JJ xDelft, NL SQUID 3JJ x xRome, Italy dcSQUID
2JJ xWork in progress: Berkeley (USA), IBM (USA)
peak and dip under -waveresonance between photon and energy spacing between lowest quantum states level repulsion
Sviluppi futuri: SQCSuperconducting
Quantum Computing
SQC è attualmente finanziato in gruppo V – end 2004
Carlo Cosmelli, Roma
ClassicalClassicalcomputer computer bitbit
1 bit two states0
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 is0 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 ∝∝ NN
•• NoNo-- Polyo il NP: o Polyo il NP: o ∝∝ ex(N)ex(N)
Ex: cτorizτio o iτeer i ri e cτors is NP Ex: cτorizτio o iτeer i ri e cτors is NP e koω oω τo solve τe role , uτ ωe do oτ ve e koω oω τo solve τe role , uτ ωe do oτ ve τe τi e !τe τi e !
Te τi e is roorτiolTe τi e is roorτiol
τo τe τo τe oo o oerτioso oerτios0 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(yers)
Yer o ricτio
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(iuτes)
Nu er o iτs
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 =ddτB
Microωves
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 comparatore
U
|>ΦL |>ΦR
Φ
U()Φ
x
Φdcx ΦΦdc
Microwaves
Flux read-outSQUI D
Quantum Information Quantum Information Technology:Technology:
Public Founding, next 5 yearsPublic Founding, next 5 years
• JapanJapan 20 M€/year20 M€/year• Europe (EC)Europe (EC) 7 M€/year + 7 M€/year + Single Single StatesStates
• USAUSA 6 M€/year + 6 M€/year + UniversitiesUniversitiesIncludes all QIT (Solid State, Photons,
Quantum Dots, Atoms, Semiconductors, Molecules, ....) for experimental and theoretical research.
World SolidWorld Solid State qubits State qubits –– Rabi Rabi obsobs..
Boulder, J J
Kansas, J J
(Maryland, J J , 2)
Saclay, Qbox
Delf t, 3J SQUI D Tsukuba, Qbox, 2
Roma, dc SQUI D