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Electronic transport in
semiconductor nanstructures
Thomas Ihn
ETH Zürich
FS 17
After this lecture you know
and understand…
•... the basics of information, bits and qubits
•... qubit implementations using quantum dots
•... the Bloch-sphere representation of a qubit
•... manipulation of charge qubits in real time
Information storage and transmission
Cuneiform inscriptions
ancient papyrus
information
transmission
through a small part
of
the internet
printed electronics
Claude Elwood Shannon
* 30. April 1916
+ 24. Februar 2001
Shannon's thesis: "possibly the
most important, and also the most
famous, master's thesis of the
century". Shannon proved that
Boolean algebra and binary
arithmetic could be used to simplify
the arrangement of the
electromechanical relays then used
in telephone routing switches, then
turned the concept upside down and
also proved that it should be possible
to use arrangements of relays to
solve Boolean algebra problems.
Exploiting this property of
electrical switches to do logic is
the basic concept that underlies
all electronic digital computers.
Analogy:
measurement and communication
Classical data storage
Surface of a CD
Magnetic domains on a hard disk
(MFM images)
RAM chip
(1 bit = 1 transistor+1capacitor)
Classical electronic information processing
From classical bits to quantum bits
classical bit
0 or 1
quantum bit
y = a 0 +b 1
0
0
1
1
needed: quantum two-level system
Possible implementations of qubits
using electrons
•
•
•
•
•
Electron far above Fermi energy
Hole deep in Fermi sea
Electron in the left/right arm of an interferometer
Electron in a quantum dot
Electron in a double quantum dot
• Electron spin (in a quantum dot)
• Singlet-Triplet states in quantum dot
Qubit: Bloch sphere representation
Established qubits in quantum dots
• Single electron spin in
one quantum dot
spin qubit
• Two energy levels in a
double quantum dot
charge qubit
• Presence/absence of an
electron-hole pair
in a single quantum dot
excitonic qubit
Quantum dot/circuit QED experiment
quantum dot
microwave resonator
resonator circuit:
superconducting aluminium
f0 = 6.75 GHz (28 meV, 280 mK)
quantum dot based: on
standard Ga[Al]As heterostructure
with 2D electron gas
T. Frey et al., PRL 108, 046807 (2012)
similar work with
single CNT-quantum dot:
M.R. Delbecq, PRL 107, 256804
(2011)
DQD current vs. resonator transmission
(M,N+1)
(M,N) (M+1,N)
Resonator
transmission :
• amplitude:
dissipation
• phase:
dispersive
T. Freyshift
et al., PRL 108, 046807 (2012)
System parameters
2t/h = 9.0 GHz
= 0.9 GHz
Coupling strength
= 50 MHz
2t/h = 6.1 GHz
= 3.3 GHz
•
Dominant decoherence is dephasing rate of 1 - 3 GHz
Single qubit manipulation
Hayashi et al.,
Phys. Rev. Lett.
91, 226804 (2003)
Free oscillations of a charge qubit
Reading
Chapter 22.1.1-3: Shannon Information, classical bits
Chapter 22.2: Thermodynamics and information
Chapter 22.3.1-3: Qubits and qubit operations