Single Electron Transistors and Quantum Computers

1. Single Electron Transistors and Quantum Computers G5: Norma L. Rangel Nanotechnology 4/20/2010

2. Overview of Nano-electronic devices Ellenbogen 2000

3. Outline • Conventional Transistors • Single Electron Transistors • Coulomb Island • Coulomb Blockade • Coulomb Gap Energy • Tunneling • Applications of SETs • Quantum Computers: NATURE, Vol 464, 03-2010

4. Transistors Fundamental component in almost all electronic devices • A transistor can be used as a switch and as amplifier • Manufactured in different shapes but they have three leads: BASE (gate controller device), COLLECTOR (larger electrical supply, source) AND EMITTER (the outlet for that supply)

5. Junction transistors & field effect transistors • A junction transistor: a thin piece of one type of semiconductor material between two thicker layers of the opposite type. • A field effect transistor: Electricity flows through one of the layers, called the channel. The voltage connected to the gate controls the strength of the current in the channel. http://www.physlink.com/Education/AskExperts/ae430.cfm

6. Single Electron Transistor (SET) Switching device that uses controlled electron tunneling to amplify current. A SET is made from two tunnel junctions that share a common electrode. An AFM picture of a single-electron transistor (SET). The red region, the island where only single electrons may be admitted. Schumacher et al.,  Applied Physics Letters

7. Single Electron Transistor (SET)Tunnel Junction • A tunnel junction consists of two pieces of  metal  separated by a very thin (~1 nm) insulator. • The only way for electrons in one of the metal electrodes to travel to the other electrode is to tunnel through the insulator. • Since tunneling is a discrete process, the electric charge that flows through the tunnel junction flows in multiples of e, the charge of a single electron.

8. Single Electron Transistor (SET)Tunneling • Quantum tunneling refers to the phenomena of a particle's ability to penetrate energy barriers within electronic structures. Schematic representation of quantum tunnelling through a barrier. The energy of the tunneled particle is the same, only the quantum amplitude (and hence the probability of the process) is decreased. http://en.wikipedia.org/wiki/Quantum_tunnelling

9. Dynamics of SET • The SET is made by placing 2 tunnel junctions in series • The 2 tunnel junction create what is known as a “Coulomb Island” that electrons can only enter by tunneling through one of the insulators. • This device has 3 terminals like the FETs. • The cap may seem like a third tunnel junction, but is much thicker than the others so that no electrons could tunnel through it. • The cap simply serves as a way of setting the electric charge on the coulomb island. controlled by light irradiation

10. Coulomb Island When a capacitor is charged through a resistor, the charge on the capacitor is proportional to the applied voltage and shows no sign of quantization. When a tunnel junction replaces the resistor, a conducting island is formed between the junction and the capacitor plate. In this case the average charge on the island increases in steps as the voltage is increased -> Low self capacitance The steps are sharper for more resistive barriers and at lower temperatures.

11. Procedure • Charge passes through the island in quantized units. • The energy must equal the coulomb energy e^2/2Cg. • Coulomb blockade, As the bias voltage between the source and drain is increased, an electron can pass through the island when the energy in the system reaches the coulomb energy. • The critical voltage needed to transfer an electron onto the island equal to e/C, is called the coulomb gap energy.

12. Coulomb Blockade • The effect in which electron can not pass through the island unless the energy in the system is equal to the coulomb energy e^2/Cg. • The thermal energy kBT must be below the charging energy or the electron will be able to pass the quantum blockade via thermal excitation • Coulomb blockade tries to alleviate any leak by current during the off state of the SET.

13. For Function SETs • Capacitance of the island must be less than 10^-17 Farads and therefore its size must be smaller that 10 nm. • The wavelength of the electrons is comparable with the size of the dot, which means that their confinement energy makes a significant contribution to the coulomb energy.

14. Example SET Fabrication • Localization of appropriate flakes with optical microscope • Contacting with metal electrodes by e-beam Lithography • Writing an etch-mask with e-beam lithography • Reactive ion etching with Ar/O2 plasma • Wire-bonding to contact pins -> testing the device • Further etching, if necessary to narrow the graphene structures

15. Example: Graphene SET • Conductance G of a device with the central island as a function of Vg in the vicinity T = 0.3 K Chaotic Dirac Billiard in Graphene Quantum Dots L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang,1 E. W. Hill, K. S. Novoselov, A. K. Geim Science 2008

16. Review Article Quantum Computers T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe & J. L. O’Brien NATURE, March 2010

17. I think I can safely say that nobody understands quantum mechanics. “No, you’re not going to be able to understand it. . . . You see, my physics students don’t understand it either. That is because I don’t understand it. Nobody does. ... The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with an experiment. So I hope that you can accept Nature as She is -- absurd. Richard Feynman

18. Quantum Computer: • A machine that would exploit the full complexity of a many-particle quantum wavefunction to solve a computational problem. • A quantum computer will not be a faster, bigger or smaller version of an ordinary computer. Rather, it will be a different kind of computer, engineered to control coherent quantum mechanical waves for different applications.

19. Light to laser - Computer to QC • Light was always ‘incoherent’, meaning that the many electromagnetic waves generated by the source were emitted at completely random times with respect to each other. • Quantum mechanical effects, however, allow these waves to be generated in phase, and the light source engineered to exploit this concept was the laser.

20. Bits and Qubits Classical Computation: Classical logic bit: “0” and “1” Quantum Computation: Quantum bit, “Qubit”, can be manipulated using the rules of quantum physics To build a quantum computer, need many qubits with long coherence times Need interactions between qubits to generate entanglement

21. Quantum State

22. Two Distinguishable States  

23. Continuous State Space a  + b  • Orthogonal quantum states |0> , |1> and their superposition |Ψ> = c0|0> + c1|1>

24. Potential technologies of QC • Shor’s quantum algorithm for factoring large numbers. Grover’s Search Algorithm • Artificial nanotechnology: we might use quantum computers to understand and engineer such technology at the atomic level. • Quantum communication: sharing of secrets with security guaranteed • Quantum metrology: in which distance and time could be measured with higher precision than is possible otherwise. • Quantum teleportation

25. Quantum teleportation • Entanglement-assisted teleportation, is a technique used to transfer quantum information from one quantum system to another. • Is a quantum protocol by which a qubit a (the basic unit of quantum information) can be transmitted exactly (in principle) from one location to another. http://en.wikipedia.org/wiki/Quantum_teleportation

26. QC Hardware • Many materials under consideration: Quantum bits are often imagined to be constructed from the smallest form of matter, an isolated atom, as in ion traps and optical lattices, but they may likewise be made far larger than routine electronic components, as in some superconducting systems. QC Software Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge University Press, 2000).

27. Implementation of quantum computers: DiVincenzo’s criteria 1. Scalability:A scalable physical system with well characterized parts, usually qubits. 2. Initialization:The ability to initialize the system in a simple “pure” state. 3. Control:The ability to control the state of the computer using sequences of elementary universal gates. 4. Stability:Long decoherence times, together with the ability to suppress decoherence through error correction and fault-tolerant computation. 5. Measurement:The ability to read out the state of the computer in a convenient product basis. DiVincenzo, Fortschr. Phys. 48, 771 (2000)

28. Dephasing and Decoherence An oscillator with frequency varying by trial, as indicated by the differently colored waves, averages to an oscillation decaying with apparent dephasing timescale T2*. A quantum oscillator interacting with the environment may have phase-kicks in a single trial; these are the processes that harm coherence in quantum computation, and lead to an average decay process of timescale T2.

29. Decoherence Qubitdecoherence can be related to noise in the environment coupled to qubit. • Relaxation of non-thermal distribution. Decay rate of resonance peaks • Dephasing caused by impedance both at level splitting and zero frequency. Width of resonance peaks

30. ERRORS • Quantum error correction’ (QEC): N • No system is fully free of decoherence, but small amounts of decoherence may be removed through various techniques • Fault-tolerant • for error probabilities beneath a critical threshold that depends on the computer hardware, the sources of error, and the protocols used for QEC.

31. Physical requirements • Scalability. The computer must operate in a Hilbert space whose dimensions can grow exponentially without an exponential cost in resources (such as time, space or energy). • Universal logic. The large Hilbert space must be accessible using a finite set of control operations; the resources for this set must also not grow exponentially. • Correctability. It must be possible to extract the entropy of the computer to maintain the computer’s quantum state. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured.

32. Technologies researchers are currently employing • Photons • Trapped Atoms • Nuclear Magnetic Resonance • Quantum Dots and dopants in solids • Superconductors • Other Technologies

33. Photons Photonic quantum circuit • Photons are relatively free of the decoherence • Allow the encoding of a qubit on the basis of location and timing; quantum information may also be encoded in the continuous phase and amplitude variables of many-photon laser beams. • Research Focus: High efficiency single-photon detectors and sources, devices that would enable a deterministic interaction between photons, and chip-scale waveguide quantum circuits. Green lines show optical waveguides; yellow components are metallic contacts.

34. Trapped atoms • The best time and frequency standards are based on isolated atomic systems. • The energy levels in trapped atoms form very reliable qubits, with T1 and T2 times typically in the range of seconds and longer. • Individual atomic ions can be confined in free space with nanometer precision using appropriate electric fields from nearby electrodes Multi-level linear ion trap chip; the inset displays a linear crystal of several ions fluorescing when resonant laser light is applied (the ion–ion spacing is 4 mm in the figure).

35. Neutral atoms • An array of cold neutral atoms may be confined in free space by a pattern of crossed laser beams, forming an optical lattice • Adjacent atoms can be brought together depending on their internal qubit levels with appropriate laser forces, and through contact interactions. Schematic of optical lattice of cold atoms formed by multi-dimensional optical standing wave potentials (J. V. Porto). Image of individual Rb atoms confined in a two-dimensional optical lattice, with atom–atom spacing of 0.64 mm (M. Greiner).

36. Nuclear Magnetic Resonance (NMR) • Nuclear spins in molecules in liquid solutions • Rapid molecular motion helps nuclei maintain their spin orientation for T2 times of many seconds. • Immersed in a strong magnetic field, nuclear spins can be identified. • Irradiating the nuclei with resonant radio-frequency pulses allows manipulation of nuclei of a distinct frequency, giving generic one-qubit gates. • Two-qubit interactions arise from the indirect coupling mediated through molecular electrons.

37. => Nuclear Spin • A nucleus with an odd atomic number or an odd mass number has a nuclear spin. • The spinning charged nucleus generates a magnetic field.

38. Two Energy States The magnetic fields of the spinning nuclei will align either with the external field, or against the field. A photon with the right amount of energy can be absorbed and cause the spinning proton to flip.

39. NMR spectrometry A 900MHz NMR instrument with a 21.2 T magnet at HWB-NMR, Birmingham, UK • http://en.wikipedia.org/wiki/NMR_spectroscopy • Chapter 13, Nuclear Magnetic Resonance Spectroscopy Organic Chemistry, 5th Edition L. G. Wade, Jr.

40. Quantum dots and dopants in solids • Motivation: A complication of using single atoms in vacuum is the need to cool and trap them. Need to be integrated into a solid-state host. • Problem: Self-assembled dots are randomly located their optical characteristics vary from dot to dot. • Rapid optical initialization has been demonstrated for both electrons and holes. • Qubits may be controlled very quickly, on the order of picoseconds, potentially enabling extremely fast quantum computers.

41. Electrostatically defined quantum dots, where the confinement is created by controlled voltages on lithographically defined metallic gates. Operate at very low temperatures (~1K) and are primarily controlled electrically, • Self-assembled quantum dots, a random semiconductor growth process creates the potential for confining electrons or holes. operate at higher temperatures (~4 K) and are primarily controlled optically.

42. Optically active solid-state dopants • The negatively charged state of the nitrogen vacancy centre forms a triplet spin system. • Under optical illumination, spin-selective relaxations facilitate efficient optical pumping of the system into a single spin state, allowing fast (250 ns) initialization of the spin qubit. • The spin state of a N-vacancy centre may then be coherently manipulated with resonant microwave fields, and then detected in a few milliseconds via spin-dependent fluorescence in an optical microscope The atomic structure of a nitrogen-vacancy centre in the diamond lattice, with lattice constant 3.6A Å.

43. Arrays of electrostatically defined dots • Each containing a single electron whose two spin states provide a qubit • Quantum logic would be accomplished by changing voltages on the electrostatic gates to move electrons closer and further from each other, activating and deactivating the exchange interaction • The single-electron transistor or quantum point contact allows the measurement of a single electron charge • The control of individual spins has also been demonstrated via direct generation of microwave magnetic and electric fields.

44. Other technologies • The carbon-based nanomaterials of fullerenes, nanotubes and graphene have excellent properties for hosting arrays of electron-based qubits. • Electrons for quantum computing may also be held in a low-decoherence environment on the surface of liquid helium, or be contained in molecular magnets Schematic diagram of a graphene double quantum dot. Each dot is assumed to have length L and width W. The structure is based on a ribbon of graphene (grey) with semiconducting armchair edges (white). Trauzettel, B., Bulaev, D. V., Loss, D. & Burkard, G. Spin qubits in graphenequantum dots. Nature Phys. 3, 192–196 (2007).

45. Comparing coherence times:

46. Status of QC • Rudimentary Quantum Computers exist • December 19, 2001 – IBM performs Shor’s Algorithm • Quantum computing is so complex that expanding on simple operations is still 10 –20 years away. • Most well known QC’s based on nuclear magnetic resonance (NMR).

47. Future Work • Promising techniques for improving coherence times • The central challenge in actually building quantum computers is maintaining the simultaneous abilities to control quantum systems, to measure them, and to preserve their strong isolation from uncontrolled parts of their environment.

48. Thanks Questions?

49. G5Rebuttal: Quantum mechanical devices Norma L. Rangel

50. Norma Rangel – Rebuttal • The featured paper (review) was very recent and potentially interesting to the audience. Although a bit unorganized, the slides had a fair amount of information and graphics. However, some references were missing or incomplete • Certainly, there were not references in every slide, but somewhere all the sources were cited in the ppt. • I know the topic was hard, but the speaker constantly apologized instead of focusing on giving her best effort, projecting confidence and credibility. The speaker gave the impression of not having a good enough knowledge of the basic theory behind the presented technology, although might rather be lack of confidence handling this specific topic. • I apologize (again) for my lack of confidence, certainly more time was require from myself to successfully cover this topic since it was not in my confidence field. • A friendlier outline of the presentation would have helped a lot. The sequence of slides was not optimal. For instance, after three slides talking about SET, there was one slide with the schematics of quantum tunneling, where actually the instructor had to intervene to explain it. It would have been better start with slide explaining quantum tunneling , and then follow with the device that uses that principle. • I fully agree with the reviewer, an outline could have been very helpful but I didn’t use it because I tried to cover two main topics: SET and QC, most of the remaining the topics came out from definitions that I found appropiate to help the audience understand the lecture.