Change and uncertainty in quantum optics

Doron ludwin, Y. Ben-Aryeh, A. Mann

We discuss complementarity and uncertainty in a gedanken Which-Way (Welcher-Weg) experiment in a Mach-Zehnder interferometer. Although a Welcher-Weg measurement can be performed with only a negligible amount of momentum change in the detector itself, the change in the interference pattern must correspond to a change in the momentum distribution of the particle. Entanglement between the Mach-Zehnder interferometer and the Welcher-Weg measurement introduces orthogonality that disables the interference of the particle, but simultaneously, it also generates a momentum transfer between the particle and other parts of the whole entangled system (including macroscopic parts). This analysis can be related to the Delayed Choice interpretation. We show where the momentum change takes place and we conclude that entanglement is the key to understand how complementarity (i.e. Which Way versus interference) and the position-momentum uncertainty relation are interwoven.

H. J. Carmichael, Roy J. Glauber, Marlan O. Scully

M. Sebawe Abdalla, R. K. Colegrave

The Kanai-Caldirola (Bateman) Hamiltonian is used to derive the dynamics of a simple harmonic oscillator, initially in a minimum uncertainty state, under the influence of an external agency which causes the mass parameter to change from ${\mathit{M}}_{0}$ to ${\mathit{M}}_{1}$ in a short time \ensuremath{\epsilon}. Then the frequency changes from ${\mathrm{\ensuremath{\omega}}}_{0}$ to ${\mathrm{\ensuremath{\omega}}}_{1}$=(${\mathit{M}}_{0}$/${\mathit{M}}_{1}$)${\mathrm{\ensuremath{\omega}}}_{0}$+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$). In the limit \ensuremath{\epsilon}\ensuremath{\rightarrow}0, no squeezing or loss of coherence occurs. If ${\mathit{M}}_{1}$/${\mathit{M}}_{0}$=1\ifmmode\pm\else\textpm\fi{}\ensuremath{\eta} (0\ensuremath{\ll}1), then a squeezing of order ${\mathrm{\ensuremath{\epsilon}}}^{2}$\ensuremath{\eta} occurs. If ${\mathit{M}}_{1}$/${\mathit{M}}_{0}$ is appreciably different from unity, then the quadrature variances are unequal but the state no longer has minimum uncertainty. An application could be made in quantum optics.

H. J. Carmichael, Roy J. Glauber, Marlan O. Scully

S. M. F. Raupach, Andreas Koczwara, Gesine Grosche

Optical frequency transfer with record-high accuracy ($1\ifmmode\times\else\texttimes\fi{}{10}^{-20}$ uncertainty) is realized over a 1400km loop of underground fiber between Braunschweig and Strasbourg, which enables reliable comparison of state-of-the-art atomic clocks that are accurate enough to detect changes in the fabric of space-time.

Subhashish Banerjee, Arun M. Jayannavar