Page 173 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 161

The concept consists in exploiting the inherent entanglement of
superconducting Cooper pair together with electron-electron interactions in
one dimension to enable the sequential injection of entangled pairs from a
superconductor into two nanotubes located next to each other at a distance
well below the Cooper pair coherence length. The key to the Cooper pair
injection and separation into entangled electrons relies on the Lüttinger
liquid behavior exhibited by CNTs characterized by an interaction factor g
and subband spacing ε . In particular [189], the tunneling rate,
0
1
1 −
Γ ~ (eV h )(kT İ )g , at which Cooper pairs tunnel from the
AA 0
superconductor into the end of a CNT, being proportional to eVρ , turns
2 e
1 § 1 · ¸
out to be much smaller than the tunneling rate Γ ~ (eV h )(kT İ ) © g2 ¨ −1 ¸ ¹ ,
¨
AB 0
at which split entangled pairs are injected into both CNTs. This difference, is
rooted in the fact that Lüttinger liquid behavior, manifested as the coherent
arrangement of all electrons in the CNT bulk, causes the single-electron
1 § 1 · ¸
ρ
tunneling density of states, () ~E ε −1 ( εE ) © g4 ¨ −1 ¸ ¹ to dominate the Cooper
¨
e 0 0
1
pair tunneling density of states, ρ () ~E ε − 1 (E ε )g . With Γ << Γ ,
2 e 0 0 AA AB
virtually all the charge tunneling that occurs involves split entangled pairs.
Once split, the entangled electrons may propagate for long distances due
to the ballistic property that characterizes transport in CNTs of Fermi
velocity v and length L at low temperatures T < T = v = k L at which
F φ F B
loss of coherence due to thermal effects are nonexistent.

4.3.1 Quantum Computing Paradigms

As indicated in Chapter 2, the fundamental building block on which
quantum information processing systems are based is the qubit, a two-state
quantum system. Qubits may take on many physical forms, however, to be
useful in realizing real, practical, systems, they must be endowed with three
key properties [190]: 1) They must be decoupled from the environment to
avoid disturbances which may deviate their time evolution from unitarity; 2)
They must be able to respond, in a controlled fashion, to purposeful
manipulation, in order to enable the formation of quantum logic gates and
entangled states, which rely on such interactions; 3) They must withstand the
momentary, but strong, coupling to the environment introduced by a
measuring device. In this section, we present the principles of various qubit
implementations, in particular, ion-trap-, nuclear-magnetic resonance-, solid-
state-, and superconducting-based qubits.