High-precision quantum parameter estimation is fundamental to the advancement of quantum metrology. Although reservoir engineering provides a powerful approach to improve estimation by tailoring system-environment interactions, the role of the squeezing phase and correlations arising from the sequential utilization of the same squeezed reservoir remains inadequately explored. In this work, we employ a correlated squeezed-thermal reservoir to enhance the precision of estimating the phase parameter
φ and the correlation factor
μ, both individually and simultaneously. We show that the squeezing phase
Φ is crucial for achieving quantum-enhanced precision, with optimal phase-matching conditions that depend strongly on
μ. Specifically, we derive the near-optimal phase-matching relations aimed at maximizing the quantum Fisher information (QFI) for both
φ and
μ, as well as minimizing the total variance
Δsim in joint estimation. Furthermore, we show that the joint estimation variance is dominated by
Fφ, which motivates our search for the phase-matching conditions that minimize
Δsim. Through the ratio
R of variances, we demonstrate that joint estimation conserves quantum resources and maintains high precision when the squeezing phase is optimized for
Fφ, despite the inherent incompatibility of the parameters. These findings provide practical insights into reservoir engineering strategies for high-precision quantum sensing and information processing.
This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing parameter, phase difference, and coupling strength within an Ohmic spectral density model. The decoherence factor shows how reservoir engineering influences coherence loss. Numerical results demonstrate that optimal squeezing and local bath configurations enhance QFI preservation, while collective couplings accelerate decay. We also examine the interplay with von Neumann entropy, highlighting their inverse correlation, where increased mixedness reduces metrological sensitivity.
As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. It was reported that N two-level systems (TLSs) located near a one-dimensional waveguide can generate SS by using the mediation effect of the waveguide. However, a coherent driving on each TLS is used to stabilize the SS, which raises a high requirement for experiments. We here propose a scheme to generate stable SS resorting to neither the spin-spin coupling nor the coherent driving on the TLSs. Incorporating the mediation role of the common waveguide and the technique of squeezed-reservoir engineering, our scheme exhibits the advantages over previous ones in the scaling relation of the SS parameter with the number of the TLSs. The long-range correlation feature of the generated SS along the waveguide in our scheme may endow it with certain superiority in quantum sensing, e.g., improving the sensing efficiency of spatially unidentified weak magnetic fields.
Squeezing a quantum state along a specific direction has long been recognized as a crucial technique for enhancing the precision of quantum metrology by reducing parameter uncertainty. However, practical quantum metrology often involves the simultaneous estimation of multiple parameters, necessitating the use of high-quality squeezed states along multiple orthogonal axes to surpass the standard quantum limit for all relevant parameters. In addition, a temporally stabilized squeezed state can provide an event-ready probe for parameters, regardless of the initial state, and robust to the timing of the state preparation process once stabilized. In this work, we generate and stabilize a two-mode squeezed state along two secular motional modes in a vibrating trapped ion with reservoir engineering, despite starting from a thermal state of the motion. Leveraging this resource, we demonstrate an estimation of two simultaneous collective displacements along the squeezed axes, achieving improvements surpassing the classical limit by up to 6.9(3) and 7.0(3) decibels (dB), respectively. Our demonstration can be readily scaled to squeezed states with even more modes. The practical implications of our findings span a wide range of applications, including quantum sensing, quantum imaging, and various fields that demand precise measurements of multiple parameters.
The interaction of an atomic two-level system and a squeezed vacuum leads to interesting effects in atomic dynamics, including line narrowing in resonance fluorescence and absorption spectra, and a suppressed (enhanced) decay of the in-phase and out-of-phase components of the atomic polarization. On the experimental side these predictions have so far eluded observation, essentially due to the difficulty of embedding atoms in a $4\ensuremath{\pi}$ squeezed vacuum. In this paper we show how to ``engineer'' a squeezed-bath-type interaction for an effective two-level system. In the simplest example, our two-level atom is represented by the two ground levels of an atom with an angular momentum $J=1/\stackrel{\ensuremath{\rightarrow}}{2}J=1/2$ transition (a four-level system), which is driven by (weak) laser fields and coupled to the vacuum reservoir of radiation modes. Interference between the spontaneous emission channels in optical pumping leads to a squeezed-bath-type coupling and thus to symmetry breaking of decay on the Bloch sphere. With this system it should be possible to observe the effects predicted in the context of squeezed-bath--atom interactions. The laser parameters allow one to choose properties of the squeezed-bath interaction, such as the (effective) photon-number expectation number
N and the squeezing phase $\ensuremath{\varphi}$. We present results of a detailed analytical and numerical study.
This study explores the dual role of a squeezed reservoir in controlling the quantum phase synchronization of a driven two-level system. We first demonstrate, through a Liouvillian eigen-spectrum analysis, that the squeezed reservoir can induce a stable limit cycle, transforming the passive TLS into a genuine self-sustained oscillator. This enables a qualitative transition from a weak ``forced response" to a robust, high-quality synchronization (or entrainment). This enhancement is characterized not only by a greater degree of phase locking but also by an increased frequency selectivity, manifested as a narrower Arnold tongue. More strikingly, we reveal that the squeezing angle acts as a control parameter to actively suppress synchronization. By tuning this angle, the reservoir can drive the system into a classical mixed state, inducing a quantum synchronization blockade via the quenching of steady-state coherence. Our findings establish squeezed-reservoir engineering as a versatile strategy for actively modulating quantum synchronization, with feasible implementations in circuit quantum electrodynamics.