Electronic transport in semiconductor nanstructures Thomas Ihn ETH

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+1 capacitor)

Classical electronic information processing

From classical bits to quantum bits classical bit quantum bit 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 circuit: superconducting aluminium f 0 = 6. 75 GHz (28 me. V, 280 m. K) quantum dot based: on standard Ga[Al]As heterostructure with 2 D electron gas T. Frey et al. , PRL 108, 046807 (2012) similar work with single CNT-quantum dot: M. R. Delbecq, PRL 107, 256804

DQD current vs. resonator transmission (M, N+1) (M, N) (M+1, N) Resonator transmission : • amplitude: dissipation • phase: dispersive shift T. Frey et al. , PRL 108, 046807

System parameters 2 t/h = 9. 0 GHz = 0. 9 GHz Coupling strength = 50 MHz 2 t/h = 6. 1 GHz = 3. 3 GHz • Dominant decoherence is dephasing rate of 1 - 3 GHz

Strong coupling regime detuning d

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