We investigate the problem of estimating the tunneling frequency of a two-level atomic system embedded in a dissipative environment by employing a numerically rigorous hierarchical equations-of-motion method. The effect of counter-rotating-wave terms on the attainable precision of the noisy quantum metrology is systematically studied beyond the usual framework of perturbative treatments. We find the counter-rotating-wave terms are able to boost the noisy quantum metrological performance in the intermediate- and strong-coupling regimes, whether the dissipative environment is composed of bosons or fermions. The results presented in this paper may pave the way to design a high-precision quantum estimation scenario under practical decoherence.
We investigate the problem of estimating the tunneling frequency of a two-level atomic system embedded in a dissipative environment by employing a numerically rigorous hierarchical equations-of-motion method. The effect of counter-rotating-wave terms on the attainable precision of the noisy quantum metrology is systematically studied beyond the usual framework of perturbative treatments. We find the counter-rotating-wave terms are able to boost the noisy quantum metrological performance in the intermediate- and strong-coupling regimes, whether the dissipative environment is composed of bosons or fermions. The results presented in this paper may pave the way to design a high-precision quantum estimation scenario under practical decoherence.
We investigate the performance of quantum parameter estimation based on a qubit probe in a dissipative bosonic environment beyond the traditional paradigm of weak-coupling and rotating-wave approximations. By making use of an exactly numerical hierarchical equations of motion method, we analyze the influences of the non-Markovian memory effect induced by the environment and the form of probe-environment interaction on the estimation precision. It is found that (i) the non-Markovianity can effectively boost the estimation performance and (ii) the estimation precision can be improved by introducing a perpendicular probe-environment interaction. Our results indicate the scheme of parameter estimation in a noisy environment can be optimized via engineering the decoherence mechanism.
We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic or a fermionic environment with a detuned Lorentz spectrum at zero temperature is analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity whether the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.
Quantum metrology offers enhanced performance in experiments on topics such as gravitational wave-detection, magnetometry or atomic clock frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features, such as entanglement or squeezing. For any practical application, the inevitable impact of decoherence needs to be taken into account in order to correctly quantify the ultimate attainable gain in precision. We compare the applicability and the effectiveness of various methods of calculating the ultimate precision bounds resulting from the presence of decoherence. This allows us to place a number of seemingly unrelated concepts into a common framework and arrive at an explicit hierarchy of quantum metrological methods in terms of the tightness of the bounds they provide. In particular, we show a way to extend the techniques originally proposed in Demkowicz-Dobrzański et al (2012 Nature Commun. 3 1063), so that they can be efficiently applied not only in the asymptotic but also in the finite number of particles regime. As a result, we obtain a simple and direct method, yielding bounds that interpolate between the quantum enhanced scaling characteristic for a small number of particles and the asymptotic regime, where quantum enhancement amounts to a constant factor improvement. Methods are applied to numerous models, including noisy phase and frequency estimation, as well as the estimation of the decoherence strength itself.
We use an analytical method to study the dissipative dynamics of a two-level system (TLS) under a harmonic driving. The method is based on a combination of the unitary transformation and Born--Markov master-equation approach. Our main aim is to clarify the effects of counter-rotating (CR) terms of both the driving and TLS-bath (dissipative) coupling on the dynamics, in comparison with the rotating-wave results of different schemes, i.e., the well-known traditional rotating-wave approximation method, and two particular methods: one just takes into account the effects of the driving CR terms and the other the effects of the dissipative CR terms, which are derived from our general treatment. Our main results are as follows: (i) by calculating the time-dependent population difference and coherence, in the case of resonant strong driving, we demonstrate that the CR terms of both the driving and dissipative coupling play an important role in the relaxation and dephasing processes, and also the properties of the steady state; (ii) in the case of largely detuned driving, we find that the CR terms of the dissipative coupling become negligible while those of the driving contribute dominant modifications to the time evolution and steady state. Moreover, we examine the influence of the dissipation on coherent destruction of tunneling under a largely detuned strong driving. We show that an almost complete suppression of the tunneling can be achieved for a relatively long time; (iii) under certain conditions, we find numerical equivalence between one of two particular methods and the Floquet--Born--Markov approach based on exact numerical treatment of the Floquet Hamiltonian. It turns out that our method is more simple and efficient than the Floquet--Born--Markov approach for both analytical and numerical calculations. By the general comparison of different treatments we demonstrate the dynamical effects of CR terms of both the driving and the dissipative coupling on the coherence and population difference.
Quantum metrology promises precision beyond classical limits, yet environmental noise typically degrades the quantum resources required for such enhancement. In this work, we investigate frequency estimation in noisy continuous-variable systems, focusing on two complementary strategies to mitigate decoherence: Hamiltonian engineering and the exploitation of non-Markovian dynamics. By embedding squeezing directly into the system Hamiltonian, we show that the quantum Fisher information (QFI) may acquire a tunable higher-order time dependence, leading to enhanced sensitivity in the short-time regime. Moving beyond the Markovian approximation, we employ the quantum Brownian motion model to demonstrate that structured environments with finite memory can induce information backflow, temporarily restoring and even improving estimation precision relative to the unitary limit. We further assess the achievability of these bounds via Gaussian measurements, identifying regimes where homodyne, heterodyne, and optimized general-dyne measurements saturate the QFI, and noting that stronger squeezing widens the gap, potentially requiring non-Gaussian measurement strategies. Our results establish that jointly tailoring system Hamiltonian and environmental memory offers a viable route toward robust quantum-enhanced frequency estimation in open systems.
We investigate the dynamics of a driven two-level system (classical Rabi model) using the counter-rotating-hybridized rotating-wave method (CHRW), which is a simple method based on a unitary transformation with a parameter $\ensuremath{\xi}$. This approach is beyond the traditional rotating-wave approximation (Rabi-RWA) and more importantly, remains the RWA form with a renormalized tunneling strength and a modified driving strength. The reformulated rotating-wave method not only possesses the same mathematical simplicity as the Rabi-RWA but also allows us to explore the effects of counter-rotating (CR) components. We focus on the properties of off-resonance cases for which the Rabi-RWA method breaks down. After comparing the results of different RWA schemes and those of the numerically exact method in a wide range of parameter regime, we show that the CHRW method gives the accurate driven dynamics which is in good agreement with the numerical method. Moreover, the other RWA methods appear as various limiting cases of the CHRW method. The CHRW method reveals the effects of the CR terms clearly by means of coherent destruction of tunneling and Bloch-Siegert shift. Our main results are as follows: (i) the dynamics of the coherent destruction of tunneling is explicitly given and its dependence on $\ensuremath{\Delta}$ is clarified, which is quantitatively in good agreement with the exact results; (ii) the CR modulated Rabi frequency and the Bloch-Siegert shift are analytically calculated, which is the same as the exact results up to fourth order; (iii) the validity of parameter regions of different RWA methods are given and the comparison of dynamics of these methods are shown. Since the CHRW approach is mathematically simple as well as tractable and physically clear, it may be extended to some complicated problems where it is difficult to do a numerical study.