arXiv:1811.02412 · Physical Review A

Phase sensitivity of a Mach-Zehnder interferometer with single-intensity and difference-intensity detection

Stefan Ataman, Anca Preda, Radu Ionicioiu

Published Oct 30, 2018• 64 citations

Abstract

Interferometry is a widely used technique for precision measurements in both classical and quantum contexts. One way to increase the precision of phase measurements, for example, in a Mach-Zehnder interferometer (MZI), is to use high-intensity lasers. In this paper we study the phase sensitivity of a MZI in two detection setups (difference intensity detection and single-mode intensity detection) and for three input scenarios (coherent, double coherent, and coherent plus squeezed vacuum). For the coherent and double coherent input, both detection setups can reach the quantum Cram\'er-Rao bound, although at different values of the optimal phase shift. The double coherent input scenario has the unique advantage of changing the optimal phase shift by varying the input power ratio.

DOI: 10.1103/physreva.98.043856

Related papers

Enhanced phase sensitivity of the Mach-Zehnder-type phase-shifting interferometry with single-intensity and difference-intensity detection

Huanrong He, Yu Zhang

Phase-shifting interferometry (PSI) promises excellent performance for quantitative phase measurement. However, the PSI is commonly realized by utilizing the Mach-Zehnder interferometer (MZI) fed with classical resources, and hence its phase sensitivity is hindered by the photon shot noise. In this paper, we propose to introduce specific phase-shifting algorithms into the well-established quantum-enhanced MZI, seeded by coherent and squeezed vacuum states and followed by single-mode intensity detection and difference intensity detection, to achieve quantitative phase measurement with sensitivity beyond that achieved by the corresponding Mach-Zehnder-type PSI with classical input. We show that when the average photon number of the coherent state is dominant, the optimal phase sensitivity of the Mach-Zehnder-type PSI with coherent plus squeezed vacuum input is better than the phase sensitivity of the Mach-Zehnder-type PSI with single coherent input under the same phase-sensing intensity condition in both of detection setups. We also show that for the typical MZI seeded with a high-power coherent state and a finitely squeezed vacuum state, the combination of intensity detection and phase-shifting algorithm can still improve the sensitivity of quantitative phase measurement. Furthermore, we derive the phase sensitivity of the fixed MZI as well as the quantum Cramér-Rao bound for two detection schemes. Finally, we explore the impacts of photon losses on the phase sensitivity enhancements of the Mach-Zehnder-type PSI and the fixed MZI in the high-intensity regime for each detection setup. The robustness to losses is compared between the Mach-Zehnder-type PSI and the fixed MZI. Our results may be helpful to promote the exploration of quantum-enhanced quantitative phase sensing.

Optics ExpressJul 17, 20260 citations

Robust phase sensitivity in Mach-Zehnder interferometer using photon added and subtracted squeezed coherent state

Shivani Singh, Priya Malpani, Anirban Pathak

For the precision-based measurements, Mach-Zehnder interferometry is a widely used technique. There are various ways to enhance the precision of Mach-Zehnder interferometer (MZI), e.g., having a non-classical input state is one of the ways to enhance the precision of the phase estimation performed by MZI. The phase estimation performed by MZI is investigated here by considering that the input states of MZI are different combinations of photon added and subtracted squeezed coherent states (PASCS and PSSCS). Using quantum Fisher information, it is shown that the use of PASCS in both the input modes of MZI, provides the most precise estimate of the unknown phase. This system is also analyzed in two different measurement scenarios -- single intensity detection (SID) and intensity difference detection (IDD). Systematic analysis has established that the intensity measurement might not be an optimal measurement scheme for phase estimation in MZI as phase and intensity correspond to non-commuting observables. The impact of the photon loss on the MZI-based phase estimation setup is also studied and it is found that PASCS is robust against photon loss, when the loss in MZI is low.

quant-pharXiv:2607.02984Jul 6, 20260 citations

Enhancing phase sensitivity in a Mach-Zehnder interferometer with various detection schemes using SU(1,1) coherent states

Nour-Eddine Abouelkhir, Abdallah Slaoui, El Hassan Saidi +2 more

Improving interferometric phase sensitivity is crucial for high-precision measurements in rapidly developing quantum technologies. The Mach–Zehnder interferometer (MZI) is a versatile tool for analyzing this phenomenon. By splitting and recombining a light beam using beam splitters, the MZI allows for precise phase sensitivity analysis using tools like the quantum Cramér–Rao bound (QCRB) and the quantum Fisher information (QFI). This paper analyzes the phase sensitivity of an MZI in various scenarios using different detection schemes and input states. We compare the single- and two-parameter quantum estimation and their associated QCRB for three phase-shift situations: in both arms; only in the upper arm (asymmetric); and in both arms symmetrically. We then investigate the phase sensitivity under three detection schemes: intensity difference; single-mode intensity; and balanced homodyne. Additionally, we explore the use of Perelomov and Barut–Girardello coherent states, two types of SU(1,1) coherent states, in all scenarios. Notably, we demonstrate that, under optimal conditions, all detection schemes can achieve the QCRB by utilizing SU(1,1) coherent states as input states.

arXiv:2406.08007Journal of the Optical Society of America BDec 23, 202414 citations

Quantum-enhanced super-sensitivity of Mach–Zehnder interferometer using squeezed Kerr state

Dhiraj Yadav, Gaurav K. Shukla, Priyanka Sharma +1 more

We study the phase super–sensitivity of a Mach–Zehnder interferometer (MZI) with the squeezed Kerr state (SKS) and coherent state as the inputs. We discuss the lower bound in phase sensitivity by considering the quantum Fisher information and the corresponding quantum Cramér–Rao bound. With the help of single intensity detection, intensity difference detection, and homodyne detection schemes, we find that our scheme gives a better sensitivity under both lossless and lossy conditions as compared to the well–known results of the combinations of inputs, such as coherent plus vacuum, coherent plus squeezed vacuum, and double coherent states. Because of the possibility of the generation of SKS with the present available quantum optical techniques, we expect that SKS may be an alternative nonclassical resource for the improvement in the phase super–sensitivity of the MZI in realistic scenarios.

arXiv:2309.04731APL QuantumFeb 23, 202422 citations

Phase sensitivity with a coherent beam and twin beams via intensity difference detection

Jun Liu, Tao Shao, Chenlu Li +4 more

We focus on the Mach–Zehnder interferometer (MZI) with the input of a coherent beam and one of the bright entangled twin beams with an external power reference beam employed for measurement. The results show that the phase sensitivity can reach sub-Heisenberg limit and approach quantum Cramér–Rao bound by changing the squeezing parameters and the photon number of the coherent beam, under the phase-matching condition. The absence of the external power reference beam will degrade the performance of the phase sensitivity. Meanwhile, this scheme shows good robustness against the losses of the photon detectors. We present a detailed discussion about the phase sensitivities when the inputs are two coherent beams, or a coherent beam plus a single-mode squeezed vacuum beam based on the MZI. This scenario can be applied in the field of phase precision measurements and other optical sensors.

Chinese Physics BOct 7, 20236 citations

Enhancement of the phase sensitivity with two-mode squeezed coherent state based on a Mach-Zehnder interferometer

Jun Liu, Tao Shao, Yuanxiang Wang +4 more

We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.

Optics ExpressJul 26, 202313 citations