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Measuring quantum systems with a tunnel junction
Umeå University, Faculty of Science and Technology, Department of Physics.
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 [en]
quantum mechanics, quantum measurement, tunnel junction, qubit, nanomechanics, noise
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-951ISBN: 91-7264-237-8 (print)OAI: oai:DiVA.org:umu-951DiVA: diva2:145169
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
List of papers
1. Quantum measurement in the charge representation
Open this publication in new window or tab >>Quantum measurement in the charge representation
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
Identifiers
urn:nbn:se:umu:diva-5599 (URN)10.1103/PhysRevB.70.115327 (DOI)
Available from: 2006-12-13 Created: 2006-12-13 Last updated: 2011-03-11Bibliographically approved
2. Statistics of charge transfer in a tunnel junction coupled to an oscillator
Open this publication in new window or tab >>Statistics of charge transfer in a tunnel junction coupled to an oscillator
2005 (English)In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Physical Review B, Vol. 72, no 16, 165347- p.Article in journal (Refereed) Published
Abstract [en]

The charge transfer statistics of a tunnel junction coupled to a quantum object is studied using the charge projection technique. The joint dynamics of the quantum object and the number of charges transferred through the junction is described by the charge specific density matrix. The method allows evaluating the joint probability distribution of the state of the quantum object and the charge state of the junction. The statistical properties of the junction current are derived from the charge transfer statistics using the master equation for the charge specific density matrix. The theory is applied to a nanoelectromechanical system, and the influence on the average current and the current noise of the junction is obtained for coupling to a harmonic oscillator.

Place, publisher, year, edition, pages
New York: American institute of physics, 2005
Identifiers
urn:nbn:se:umu:diva-12005 (URN)10.1103/PhysRevB.72.165347 (DOI)
Available from: 2007-03-19 Created: 2007-03-19 Last updated: 2011-03-11Bibliographically approved
3. Noise spectrum of a tunnel junction coupled to a nanomechanical oscillator
Open this publication in new window or tab >>Noise spectrum of a tunnel junction coupled to a nanomechanical oscillator
2007 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Physical Review B, Vol. 75, no 20, 205319-13 p p.Article in journal (Refereed) Published
Abstract [en]

A nanomechanical resonator coupled to a tunnel junction is studied. The oscillator modulates the transmission of the junction, changing the current and the noise spectrum. The influence of the oscillator on the noise spectrum of the junction is investigated, and the noise spectrum is obtained for arbitrary frequencies, temperatures, and bias voltages. We find that the noise spectrum consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator frequency, and twice the oscillator frequency. The influence of the oscillator vanishes if the bias voltage of the junction is lower than the oscillator frequency. We demonstrate that the peak at the oscillator frequency can be used to determine the oscillator occupation number, showing that the current noise in the junction functions as a thermometer for the oscillator.

Place, publisher, year, edition, pages
AIP Physics, 2007
Keyword
noise, quantum physics, nanomechanics, electronic transport
National Category
Condensed Matter Physics Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-5601 (URN)10.1103/PhysRevB.75.205319 (DOI)
Available from: 2006-12-13 Created: 2006-12-13 Last updated: 2011-02-25Bibliographically approved

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