The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations of the interferometer with respect to an inertial reference frame result in a shift in the interference pattern proportional to the rotation rate. Here, we analyze the Sagnac effect in a mesoscopic semiconductor electron interferometer. We include in our analysis the Rashba spin-orbit interactions in the ring. Our results indicate that spin-orbit interactions increase the rotation-induced phase shift. We discuss the potential experimental observability of the Sagnac phase shift in such mesoscopic systems.The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations of the interferometer with respect to an inertial reference frame result in a shift in the interference pattern proportional to the rotation rate. Here, we analyze the Sagnac effect in a mesoscopic semiconductor electron interferometer. We include in our analysis the Rashba spin-orbit interactions in the ring. Our results indicate that spin-orbit interactions increase the rotation-induced phase shift. We discuss the potential experimental observability of the Sagnac phase shift in such mesoscopic systems.

arXiv:0705.0388Physical Review BMar 6, 200812 citations

Phase-controlled nonlinear interferometry

G. L�pke, Gerd Marowsky, Robert Steinhoff

Applied Physics BSep 1, 198922 citations

Sagnac effect in a chain of mesoscopic quantum rings

Christopher P. Search, John R. E. Toland, Marko Zivkovic

The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential ${10}^{10}$ enhancement of the rotational phase shift in comparison to optical Sagnac gyroscopes. Here we analyze ballistic transport of matter waves in a one-dimensional chain of $N$ coherently coupled quantum rings in the presence of a rotation of angular frequency $\ensuremath{\Omega}$. We show that the transmission probability, $T$ , exhibits zero transmission stop gaps as a function of the rotation rate interspersed with regions of rapidly oscillating finite transmission. With increasing $N$ , the transition from zero transmission to the oscillatory regime becomes an increasingly sharp function of $\ensuremath{\Omega}$ with a slope $\ensuremath{\partial}T/\ensuremath{\partial}\ensuremath{\Omega}\ensuremath{\sim}{N}^{2}$. The steepness of this slope dramatically enhances the response to rotations in comparison to conventional single ring interferometers such as the Mach-Zehnder interferometer and leads to a phase sensitivity well below the quantum shot-noise limit typical of atom interferometers.The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential ${10}^{10}$ enhancement of the rotational phase shift in comparison to optical Sagnac gyroscopes. Here we analyze ballistic transport of matter waves in a one-dimensional chain of $N$ coherently coupled quantum rings in the presence of a rotation of angular frequency $\ensuremath{\Omega}$. We show that the transmission probability, $T$, exhibits zero transmission stop gaps as a function of the rotation rate interspersed with regions of rapidly oscillating finite transmission. With increasing $N$, the transition from zero transmission to the oscillatory regime becomes an increasingly sharp function of $\ensuremath{\Omega}$ with a slope $\ensuremath{\partial}T/\ensuremath{\partial}\ensuremath{\Omega}\ensuremath{\sim}{N}^{2}$. The steepness of this slope dramatically enhances the response to rotations in comparison to conventional single ring interferometers such as the Mach-Zehnder interferometer and leads to a phase sensitivity well below the quantum shot-noise limit typical of atom interferometers.

arXiv:0810.4111Physical Review AMay 6, 200914 citations

A Mesoscopic Mach-Zehnder Interferometer

Yang Ji, Yunchul Chung, David Sprinzak +2 more

Springer eBooksDec 13, 20050 citations

The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential

{10}^{10}

enhancement of the rotational phase shift in comparison to optical Sagnac gyroscopes. Here we analyze ballistic transport of matter waves in a one-dimensional chain of

N

coherently coupled quantum rings in the presence of a rotation of angular frequency $\ensuremath{\Omega}$. We show that the transmission probability,

T

, exhibits zero transmission stop gaps as a function of the rotation rate interspersed with regions of rapidly oscillating finite transmission. With increasing

N

, the transition from zero transmission to the oscillatory regime becomes an increasingly sharp function of $\ensuremath{\Omega}$ with a slope $\ensuremath{\partial}T/\ensuremath{\partial}\ensuremath{\Omega}\ensuremath{\sim}{N}^{2}$. The steepness of this slope dramatically enhances the response to rotations in comparison to conventional single ring interferometers such as the Mach-Zehnder interferometer and leads to a phase sensitivity well below the quantum shot-noise limit typical of atom interferometers.