Robustness of Heisenberg-limited interferometry with balanced Fock states

Abstract

Interferometry with Heisenberg limited phase resolution may play an important role in the next generation of atomic clocks, gravitational wave detectors, and in quantum information science. For experimental implementations the robustness of the phase resolution is crucial since any experimental realization will be subject to imperfections. In this article we study the robustness of phase reconstruction with two number states as input subject to fluctuations in the state preparation. We find that the phase resolution is insensitive to fluctuations in the total number of particles and robust against noise in the number difference at the input. The phase resolution depends on the uncertainty in the number difference in a universal way that has a clear physical interpretation: Fundamental noise due to the Heisenberg limit and noise due to state preparation imperfection contribute essentially independently to the total uncertainty in the phase. For number difference uncertainties less than one the first noise source is dominant and the phase resolution is essentially Heisenberg limited. For number difference uncertainties greater than one the noise due to state preparation imperfection is dominant and the phase resolution deteriorates linearly with the number difference uncertainty.

arXiv comment13 pages, 6 figures; high-resolution version can be obtained from authors

References in corpus (13)

• Quantum-enhanced measurements: beating the standard quantum limit
• On the Improvement of Frequency Stardards with Quantum Entanglement
• Conversion of conventional gravitational-wave interferometers into QND interferometers by modifying their input and/or output optics
• Sr lattice clock at 1x10^{-16} fractional uncertainty by remote optical evaluation with a Ca clock
• Optimal Quantum Phase Estimation
• Optimal states and almost optimal adaptive measurements for quantum interferometry
• Experimental demonstration of a squeezing enhanced power recycled Michelson interferometer for gravitational wave detection
• ${}^{87}$Sr lattice clock with inaccuracy below 10${}^{-15}$
• Systematic study of the ${}^{87}$Sr clock transition in an optical lattice
• An accurate optical lattice clock with 87Sr atoms
• Controlling the cold collision shift in high precision atomic interferometry
• Quantum states for Heisenberg-limited interferometry
• Optimized Double-well quantum interferometry with Gaussian squeezed-states

Cited by in corpus (8)

• The elusive Heisenberg limit in quantum enhanced metrology
• How to perform the most accurate possible phase measurements
• Efficient tools for quantum metrology with uncorrelated noise
• Quantum metrology with imperfect states and detectors
• Optimal Quantum-Enhanced Interferometry
• Heisenberg-limited interferometry with pair coherent states and parity measurements
• Quantum Metrology with Dicke Squeezed States
• Globally optimal interferometry with lossy twin Fock probes