In recent work we proposed a quantum interferometer and showed how it could be used to significantly enhance the resolution that could be achieved in measurement schemes. In this paper, we outline a detailed scheme on how these quantum interferometers could be implemented. We also analyze the effects of dissipation and of imperfect detectors and show that this scheme is remarkably robust to both. This suggests that quantum interferometers may provide a promising route for implementing sub-shot-noise limited measurements in the laboratory.In recent work we proposed a quantum interferometer and showed how it could be used to significantly enhance the resolution that could be achieved in measurement schemes. In this paper, we outline a detailed scheme on how these quantum interferometers could be implemented. We also analyze the effects of dissipation and of imperfect detectors and show that this scheme is remarkably robust to both. This suggests that quantum interferometers may provide a promising route for implementing sub-shot-noise limited measurements in the laboratory.

Journal of Modern OpticsJan 10, 200624 citations

Sub-quantum-limit interferometry

Masahiro Kitagawa, Masahito Ueda

Jan 1, 19930 citations

Electron Interferences Using Macroscopic and Nanoscopic Interferometers

F. Frémont

Springer series on atomic, optical, and plasma physicsJun 15, 20131 citation

Sub-shot-noise phase sensitivity with a Bose-Einstein condensate Mach-Zehnder interferometer

Luca Pezzè, Lee A. Collins, Augusto Smerzi +2 more

Bose-Einstein condensates (BEC), with their coherence properties, have attracted wide interest for their possible application to ultraprecise interferometry and ultraweak force sensors. Since condensates, unlike photons, are interacting, they may permit the realization of specific quantum states needed as input of an interferometer to approach the Heisenberg limit, the supposed lower bound to precision phase measurements. To this end, we study the sensitivity to external weak perturbations of a representative matter-wave Mach-Zehnder interferometer whose input are two Bose-Einstein condensates created by splitting a single condensate in two parts. The interferometric phase sensitivity depends on the specific quantum state created with the two condensates, and, therefore, on the time scale of the splitting process. We identify three different regimes, characterized by a phase sensitivity $\ensuremath{\Delta}\ensuremath{\theta}$ scaling with the total number of condensate particles $N$ as (i) the standard quantum limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{1∕2}$, (ii) the sub shot-noise $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{3∕4}$, and the (iii) the Heisenberg limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕N$. However, in a realistic dynamical BEC splitting, the $1∕N$ limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub-shot-noise sensitivity $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{3∕4}$ can be reached in a realistic experimental setting. We also show that the $1∕{N}^{3∕4}$ scaling is a rigorous upper bound in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.Bose-Einstein condensates (BEC), with their coherence properties, have attracted wide interest for their possible application to ultraprecise interferometry and ultraweak force sensors. Since condensates, unlike photons, are interacting, they may permit the realization of specific quantum states needed as input of an interferometer to approach the Heisenberg limit, the supposed lower bound to precision phase measurements. To this end, we study the sensitivity to external weak perturbations of a representative matter-wave Mach-Zehnder interferometer whose input are two Bose-Einstein condensates created by splitting a single condensate in two parts. The interferometric phase sensitivity depends on the specific quantum state created with the two condensates, and, therefore, on the time scale of the splitting process. We identify three different regimes, characterized by a phase sensitivity $\ensuremath{\Delta}\ensuremath{\theta}$ scaling with the total number of condensate particles $N$ as (i) the standard quantum limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{1∕2}$, (ii) the sub shot-noise $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{3∕4}$, and the (iii) the Heisenberg limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕N$. However, in a realistic dynamical BEC splitting, the $1∕N$ limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub-shot-noise sensitivity $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{3∕4}$ can be reached in a realistic experimental setting. We also show that the $1∕{N}^{3∕4}$ scaling is a rigorous upper bound in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.

arXiv:cond-mat/0508680Physical Review AOct 26, 200568 citations

Overcoming detection inefficiency in squeezing-assisted interferometers

Gaetano Frascella, Sascha Agne, Farid Ya Khalili +1 more

Squeezing-assisted interferometers achieve sub-shot-noise sensitivity to phase shifts, but losses can strongly degrade their performance. Here we present the first experimental demonstration of detection-loss tolerance for this class of interferometers employing degenerate optical parametric amplification at one output port. For $50\%$ detection efficiency, the phase sensitivity of any interferometer with coherent and squeezed vacuum inputs would not overcome the shot-noise limit, but in our case the output amplification gives $6$ dB sub-shot-noise sensitivity. We further demonstrate that robustness increases with higher gain of the output amplifier: sub-shot-noise sensitivity is achieved for detection efficiency as low as $13\%$ . We believe that overcoming detection inefficiency will become crucial to take full advantage of quantum metrology, for example in gravitational-wave detection, quantum sensing and imaging.Squeezing-assisted interferometers achieve sub-shot-noise sensitivity to phase shifts, but losses can strongly degrade their performance. Here we present the first experimental demonstration of detection-loss tolerance for this class of interferometers employing degenerate optical parametric amplification at one output port. For $50\%$ detection efficiency, the phase sensitivity of any interferometer with coherent and squeezed vacuum inputs would not overcome the shot-noise limit, but in our case the output amplification gives $6$ dB sub-shot-noise sensitivity. We further demonstrate that robustness increases with higher gain of the output amplifier: sub-shot-noise sensitivity is achieved for detection efficiency as low as $13\%$. We believe that overcoming detection inefficiency will become crucial to take full advantage of quantum metrology, for example in gravitational-wave detection, quantum sensing and imaging.

May 18, 20200 citations

Breaking the standard quantum limit for interferometric measurements

Alfredo Luis, Luis Lorenzo Sánchez-Soto

Optics CommunicationsMay 1, 199218 citations

N

as (i) the standard quantum limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{1∕2}$, (ii) the sub shot-noise $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{3∕4}$, and the (iii) the Heisenberg limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕N$. However, in a realistic dynamical BEC splitting, the

1∕N

limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub-shot-noise sensitivity $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{3∕4}$ can be reached in a realistic experimental setting. We also show that the

1∕{N}^{3∕4}

scaling is a rigorous upper bound in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.

50\%

detection efficiency, the phase sensitivity of any interferometer with coherent and squeezed vacuum inputs would not overcome the shot-noise limit, but in our case the output amplification gives

6

dB sub-shot-noise sensitivity. We further demonstrate that robustness increases with higher gain of the output amplifier: sub-shot-noise sensitivity is achieved for detection efficiency as low as

13\%

. We believe that overcoming detection inefficiency will become crucial to take full advantage of quantum metrology, for example in gravitational-wave detection, quantum sensing and imaging.