Page 202 - Principles and Applications of NanoMEMS Physics

190 Chapter 4

affairs, two new states, ( 0 + 1 ) and ( 0 − 1 ), that are quantum
superpositions, are formed, with the energy between them now given by the
tunneling strength. Control of the qubit, such as to change its state, is
effected by coupling to the flux φ , which is accomplished by sending
current pulses on the transformer primary. Measurements of the states, made
with a superconducting quantum interference device (SQUID), a device
which consists of two Josephson junction in parallel, to detect the magnetic
flux, reveals that the currents are carried by a billion Cooper pairs, with
tunneling being the mechanism by which the directions of all of these
particles is reversed simultaneously [208]. The decoherence times, which are
s
limited by defects in the junction are in the range of 500 ns to 4µ .

4.3.1.4.3 The Phase Qubit

The phase qubit, see Fig. 4-21(c), utilizes only one Josephson junction,
and the two quantum states are embodied in the quantum oscillations of the
phase difference between junction electrodes [207]. In this case the approach
to compensating the detrimental effect of Q relies on using large ratios of
r
E / E . A large nonlinearity in the Josephson inductance is achieved by
J CJ
biasing the junction at a current ~I I . The Hamiltonian, with potential
0
shown in Fig. 4-21(f), is given by,

H = E p 2 − ϕ I δ − I ϕ cos δ . (4 )
5
CJ 0 0 0
The conjugate variables, given by the phase difference operator δ , which is
proportional to the flux across C , and the charge on the capacitance ep2 ,
J
obey the commutation relation [ ] ip,δ = [207]. The potential is
approximated by the cubic form,
I ϕ 3
V () ϕ=δ (I − )( I δ − ) 2 / π − 0 0 ( −δ ) 2 / π , (4 )
6
0 0
6
from where it can be shown that the classical frequency of oscillation at the
bottom of the well is given by,

ω = 1 ( [ 1− I I ) ] / 1 4 , (4 )
2
7
p 0
L C
0 J J
and the first two levels that can be used for the qubit states have the
transition frequency ω 01 ≅ . 0 95ω [207].
p