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Quantum measurement in the charge representation
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
2004 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 70, 115327- p.Article in journal (Refereed) Published
Abstract [en]

Counting statistics of charge transfers in a point contact interacting with an arbitrary quantum system is studied. The theory for the charge specific density matrix is developed, allowing the evaluation of the probability of the outcome of any joint measurement of the state of the quantum system and the transferred charge. Applying the method of charge projectors, the master equation for the charge specific density matrix is derived in the tunneling Hamiltonian model of the point contact. As an example, the theory is applied to a quantum measurement of a two-state system: The evolution of the charge specific density matrix in the presence of Nyquist or Schottky noise is studied and the conditions for the realization of a projective measurement are established.

Place, publisher, year, edition, pages
APS Physics , 2004. Vol. 70, 115327- p.
Identifiers
URN: urn:nbn:se:umu:diva-5599DOI: 10.1103/PhysRevB.70.115327OAI: oai:DiVA.org:umu-5599DiVA: diva2:145166
Available from: 2006-12-13 Created: 2006-12-13 Last updated: 2011-03-11Bibliographically approved
In thesis
1. Measuring quantum systems with a tunnel junction
Open this publication in new window or tab >>Measuring quantum systems with a tunnel junction
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is concerned with employing the statistics of charge transfer in a conductor as a tool for quantum measurement. The physical systems studied are electronic devices made by nanoscale manufacturing techniques. In this context quantum measurement appears not as a postulate, but as physical process. In this thesis I am considering a quantum system, in particular a qubit or a nanomechanical resonator, interacting with a tunnel junction. The effect of coupling a quantum system to a tunnel junction is twofold: The state of the quantum system will be changed and there will be information about the quantum system in the statistics of charge transfer of the tunnel junction. As the first example a quantum measurement process of a qubit is considered. A common description of the system and charge dynamics is found by introducing a new quantity, the charge specific density matrix. By deriving and solving a Markovian master equation for this quantity the measurement process is analyzed. The measurement is shown to be a dynamical process, where correlations between the initial state of the qubit and the number of charges transferred in the tunnel junction arise on a typical timescale, the measurement time. As another example of a quantum system a nanomechanical oscillator is considered. It is found, that the biased tunnel junction, acting as a non-equilibrium environment to the oscillator, increases the temperature of the oscillator from its thermal equilibrium value. The current in the junction is modulated by the interaction with the oscillator, but the influence vanishes for bias voltages smaller than the oscillator frequency. For an asymmetric junction and non-vanishing oscillator momentum a current is shown to flow through the junction even at zero bias. The current noise spectrum induced by the oscillator in the tunnel junction consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator frequency and double the oscillator frequency. The peak heights are dependent on the coupling strength between oscillator and junction, the occupation number of the oscillator, the bias voltage and the junction temperature. I show how the peak height can be used as a measure of the oscillator temperature, demonstrating that the noise of a tunnel junction can be used for electronic thermometry of a nanomechanical oscillator.

Place, publisher, year, edition, pages
Umeå: Fysik, 2006. 41 p.
Keyword
quantum mechanics, quantum measurement, tunnel junction, qubit, nanomechanics, noise
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-951 (URN)91-7264-237-8 (ISBN)
Public defence
2007-01-08, N430, Naturvetarhuset, Umeå Universitet, 901 87 Umeå, 13:15
Opponent
Supervisors
Available from: 2006-12-13 Created: 2006-12-13 Last updated: 2011-03-11Bibliographically approved

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Rammer, JörgenShelankov, Andrei L.

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