Abstract
In these lectures we will be describing the applications of quantum optical techniques to superconducting tunnel junctions. This work has been motivated, in part, by the close analogy between the quantum mechanics of BCS electron pairs in a superconducting tunnel junction and the quantum mechanics of two-level systems.1 Since two-level systems are a mainstay of quantum optics, it is natural that we begin considering problems such as coherent transients in superconducting junctions (a classic two-level system) from a quantum optical point of view. Two such problems, supperradiance and Rabi flopping effects in Josephson devices will be discussed. Some of the coherent transient effects we will see are different from those observed in the normal two-level atom problem, but there are also many similarities.
Supported by the Office of Naval Research.
This work is supported by the Air Force Office of Scientific Research (AFSC), United States Air Force, and the Army Research Office, United States Army.
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\(\vec k > 0\) means the sum is to include only those \(\vec k\)’s with kzgt;0.
With this representation we can do simple quantum mechanics of a superconductor. Everything we will deal with is at T = 0°. But to understand the physics of the Josephson problem, the (zero temperature) spinor representation is all we need.
We can see this by writing \(H = \sum\limits_{\vec k} {\left[ {{{\bar \varepsilon }_{\vec k}}\hat Z + \sum\limits_{\vec k} {V{\sigma _{{{\vec k}^\prime }x}}} \hat X} \right]} \cdot{\vec \sigma _{\vec k}}\) and noting that whereas the expectation value of the kinetic energy for the \(\vec k\)-th pair is \({\bar \varepsilon _{\vec k}}\) the expectation value of its potential energy is \( < V\sum\limits_{\vec k} {{\sigma _{k'x}} > \simeq Vm} \) (m is defined in Fig. 6).
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DiRienzo, A., Rogovin, D., Scully, M., Bonifacio, R., Lugiato, L., Milani, M. (1978). Superconductivity and Quantum Optics. In: Arecchi, F.T., Bonifacio, R., Scully, M.O. (eds) Coherence in Spectroscopy and Modern Physics. NATO Advanced Study Institutes Series, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2871-1_12
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DOI: https://doi.org/10.1007/978-1-4613-2871-1_12
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