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arXiv:1608.01493 · Optics Letters

Surpassing the shot-noise limit by homodyne-mediated feedback

Guofeng Zhang, Han‐Jie Zhu

Published Aug 12, 2016• 5 citations
arXivHTMLPDF

Abstract

Entangled systems with large quantum Fisher information (QFI) can be used to outperform the standard quantum limit of the separable systems in quantum metrology. However, the interaction between the system and the environments inevitably leads to decoherence and decrease of the QFI, and it is not clear whether the entanglement systems can be a better resource than separable systems in the realistic physical condition. In this work, we study the steady QFI of two driven and collectively damped qubits with homodyne-mediated feedback. We show that the steady QFI can be significantly enhanced both in the cases of symmetric feedback and nonsymmetric feedback, and the shot-noise limit of separable states can be surpassed in both cases. The QFI can even achieve the Heisenberg limit for appropriate feedback parameters and initial conditions in the case of symmetric feedback. We also show that an initial-condition-independent steady QFI can be obtained by using nonsymmetric feedback.

DOI
10.1364/ol.41.003932

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Entangled systems with large quantum Fisher information (QFI) can be used to outperform the standard quantum limit of the separable systems in quantum metrology. However, the interaction between the system and the environments inevitably leads to decoherence and decrease of the QFI, and it is not clear whether the entanglement systems can be a better resource than separable systems in the realistic physical condition. In this work, we study the steady QFI of two driven and collectively damped qubits with homodyne-mediated feedback. We show that the steady QFI can be significantly enhanced both in the cases of symmetric feedback and nonsymmetric feedback, and the shot-noise limit of separable states can be surpassed in both cases. The QFI can even achieve the Heisenberg limit for appropriate feedback parameters and initial conditions in the case of symmetric feedback. We also show that an initial-condition-independent steady QFI can be obtained by using nonsymmetric feedback.
Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. However the effects on the entanglement dynamics such as decoherence usually decrease the QFI considerably. On the other hand, Dzyaloshinskii-Moriya (DM) interaction has been shown to excite entanglement. Since an increase in entanglement does not imply an increase in QFI, and also there are cases where QFI decreases as entanglement increases, it is interesting to study the influence of DM interaction on quantum metrology. In this work, we study the QFI of thermal entanglement of two-qubit and three-qubit Heisenberg models with respect to SU(2) rotations. We show that even at high temperatures, DM interaction excites QFI of both ferromagnetic and antiferromagnetic models. We also show that QFI of the ferromagnetic model of two qubits can surpass the shot-noise limit of the separable states, while QFI of the antiferromagnetic model in consideration can only approach to the shot-noise limit. Our results open new insights in quantum metrology with Heisenberg models.
We consider a model of two driven and collectively damped atoms with different quantum feedbacks. We find that the steady entanglement depends on the initial condition in the case of symmetric feedback but is independent of the initial condition in the case of nonsymmetric feedback. We also find that in the process of the transition from the symmetric feedback to the nonsymmetric feedback, the entanglement between the two atoms is discontinuous. Without the feedback (symmetric case), in the symmetric subspace the steady entanglement between the two atoms will be very small; then we apply a feedback just to one of the atoms (nonsymmetric case), the steady entanglement will increase greatly, which can reach $C\ensuremath{\approx}0.82$. It is very interesting that if we withdraw the feedback, the strong steady entanglement will remain, i.e., the whole process is irreversible, and reminds us of the hysteresis phenomena.
Going beyond the standard quantum limit in noisy quantum metrology is an important and challenging task. Here we show how Dicke states can be used to surpass the standard quantum limit and achieve the Heisenberg limit in open quantum systems. The system we study has qubits symmetrically coupled to a resonator, and our objective is to estimate the coupling between the qubits and the resonator. The time-dependent quantum Fisher information with respect to the coupling is studied for this open quantum system where the same decay rates are assumed on all qubits. We show that when the system is initialized to a Dicke state with an optimal excitation number one can go beyond the standard quantum limit and achieve the Heisenberg limit even for finite values of the decays on the qubit and the resonator, particularly when the qubits and resonator are strongly coupled. We compare our results against the highly entangled GHZ state and a completely separable state and show that the GHZ state performs quite poorly, whereas under certain noise conditions the separable state is able to go beyond the standard quantum limit due to subsequent interactions with a resonator.
We investigate the quantum Fisher information (QFI) dynamics of a dissipative two-level system in homodyne-mediated quantum feedback control. The analytical results demonstrate that the maximum values and stable values of the QFI can be greatly enhanced via feedback control. The quantum feedback plays a more evident role in the improvement of classical Fisher information. The classical part can reach a high stable value, while the quantum part eventually decays to zero whatever the feedback parameter is .
Abstract A two-level atom interacting with a single-mode cavity is considered. The atom-cavity system is driven by a classical field with the homodyne-mediated feedback. The influences of the driving field and two types of the feedback on the precision of the phase estimation are investigated. The results show the quantum Fisher information (QFI) can be preserved by the homodyne-mediated feedback and the classical driving when the system parameters are suitable. In addition, the initial value of the relative phase greatly effects the QFI. Therefore, the phase estimation precision of the two-level atom can be enhanced, and the extent of the enhancement is decided by not only the driving frequency and the type of quantum feedback, but also the initial parameters of the two-level system.
Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we establish a link between the bound on the growth of the quantum Fisher information and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems. We show that for initial separable states, despite the use of local many-body interactions, the precision cannot surpass the shot noise limit at all times. This conclusion also holds for an initial state that is the nondegenerate ground state of a local and gapped Hamiltonian. These findings strongly hint that when one can only prepare separable initial states, nonlocal and long-range interactions are essential resources for surpassing the shot noise limit. This observation is confirmed through numerical analysis on the long-range Ising model. Our results bridge the field of many-body quantum sensing and operator growth in many-body quantum systems and open the possibility to investigate the interplay between quantum sensing and control, many-body physics and information scrambling.