1. 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 –

2. 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

3. 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

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

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

6. rf SQUID states: L & R
 I
U(f)
L> R> f ES EA

7. MQC (Rabi Oscillations) : QM vs. MR :
P(L,tL, t=0)  cos2 t
where = tunnelling frequency between wells
P(t) t 1
1/2

8. 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.

9. 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.

10. 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

11. 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

12. 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

13. 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 (nss).

14. 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

15. 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

16. 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)

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

18. 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 ?

19. 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

20. 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.

21. Scheme of the experimental SQUID system
dc bias
laser
SQUID Switch
Vout(f)
SQUID rf
rf bias
SQUID Amplifier

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

23. 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

24. 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

25. 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

26. 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

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

28. Readout with a hysteretic dc-SQUIDFR 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

29. Utilizzo di un dc-SQUID per la misura non invasiva dello SQUID rfFR
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

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

31. 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

32. 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.

33. 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
2c

34. Experimental results e0 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
e0
(C. Cosmelli et al. Phys. Rev. Lett. 1999)

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

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

37. Physical implementation – Measurement set up
T=300K

38. 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

39. 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

40. 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

41. 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

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

43. 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)

44. 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

45. 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

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

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

48. 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

50. 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

51. 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

52. 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

53. Quantum Information Technology: Public Founding, next 5 years
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