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arXiv:1406.7626 · New Journal of Physics

Quantum metrology with Dicke squeezed states

Z Zhang, L M Duan

Published Oct 24, 2014• 67 citations
arXivHTMLPDF

Abstract

We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing , which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as attains the minimum in an ideal Dicke state. Compared with other entangled states, we show that the DS states are more robust to decoherence and give better measurement precision under typical experimental noise.

DOI
10.1088/1367-2630/16/10/103037

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We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing , which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as attains the minimum in an ideal Dicke state. Compared with other entangled states, we show that the DS states are more robust to decoherence and give better measurement precision under typical experimental noise.
In this dissertation we focused on some quantum states with strong entanglement and robustness to noise. We constructed a spinor BEC Hamiltonian which has already been realized in experiment with several different kinds of atoms and proposed an adiabatic passage method to produce the maximal entangled Dicke state. We also analyzed the entanglement behavior of the Dicke state under various noises and demonstrate its use in high precision measurement experiment. We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing, which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as the Dicke squeezing parameter attains the minimum in an ideal Dicke state. Compared with other entangled states, we show that the Dicke squeezed states are more robust to decoherence and give better measurement precision under typical experimental noise. On the other hand, we explore other choices of precision measurement with spin squeezed states. Spin squeezed states have strong manybody entanglement and are good candidates to be used in quantum metrology. A robust squeezing parameter is proposed to characterize the experimental phase measurement precision for spin squeezed states. The behavior of this parameter under various experimental noises is compared with other parameters in the history and it is shown to have better performance. Finally we present a scalable implementation scheme for Boson sampling using local transverse phonon modes in trapped ion system, which is a promising model for quantum computers.
Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision. When particles in a probe are prepared into a suitable quantum entangled state, they may collectively accumulate information about the physical quantity to be measured, leading to an improvement in measurement precision beyond the standard quantum limit and approaching the Heisenberg limit. The rapid advancement of techniques for quantum manipulation and detection has enabled the generation, manipulation, and detection of multi-particle entangled states in synthetic quantum systems such as cold atoms and trapped ions. This article aims to review and illustrate the fundamental principles and experimental progresses that demonstrate multi-particle entanglement for quantum metrology, as well as discuss the potential applications of entanglement-enhanced quantum sensors.
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Quantum entanglement between particles is expected to allow one to perform tasks that would otherwise be impossible. In quantum sensing and metrology, entanglement is often claimed to enable a measurement precision that cannot be attained with the same number of particles and time, forgoing entanglement. Two distinct approaches exist: creation of entangled states that either i) respond quicker to the signal, or ii) are associated with lower noise and uncertainty. The second class of states are generally called squeezed states. Here we show that if our definition of success is a precision that is impossible to achieve using the same resources but without entanglement then squeezed states cannot succeed. In doing so we show that a single non-separable squeezed state provides fundamentally no better precision, per unit time, than a single particle.
Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single N+1N+1N+1 dimensional qudit that achieve precision equivalent to symmetrically entangled states on NNN qubits, showing that entanglement is not necessary for going beyond the standard quantum limit. We define a measure of non-classicality based on quantum Fisher information and estimate the achievable precision, suggesting a close relationship between non-classical states and metrological power of qudits. Our work offers an exponential reduction in the physical resources required for quantum-enhanced parameter estimation, making it accessible on any quantum system with a high-dimensional Hilbert space.
Quantum correlations can be harnessed to improve the precision in parameter estimation beyond classical capabilities. Under a standard interferometric or rotation protocol, it is well established that the optimal single-mode Gaussian state is a standard squeezed vacuum, which enables Heisenberg limited precision. In this work, we investigate the potential metrological advantage of two distinct families involving high-order squeezing, namely, mth-phase and multisqueezed states. Our results show that these non-Gaussian states can grant a significant metrological advantage with respect to the optimal squeezed vacuum under equivalent conditions, i.e. at equal occupations. Their advantage holds both at low and large occupations, but its behavior critically depends on the chosen family of high-order squeezing. While higher squeezing orders enhance the advantage, this comes at the cost of higher-order observables in the measurement for full metrological performance. Finally, we study their robustness to standard decoherence channels, i.e. pure dephasing and zero-temperature damping. Employing standard squeezing as reference state, our results indicate a reasonable robustness against damping up to a certain noise strength, while their metrological advantage becomes fragile under pure dephasing. Our work shows the potential enhancement in quantum metrology beyond Gaussian states, carefully detailing the main challenges and limitations.