Abstract:

Quantum metrology aims to harness the power of quantum mechanics to make ultra-precise measurements. A crucial advantage of quantum metrology is that it provides high precision with a significantly lower particle flux. This is an important requirement for many applications such as in biological sensing [3], where disturbing the system can damage the sample, or in gravitational wave detection [4], where the lasers in the interferometer interact with the mirrors enough to degrade the measurement [5]. It is known that an interferometer that utilizes a stream of independent particles is capable of measurement precision at the shot noise limit (SNL) 1=pn where n is the total number of particles used in the probe state. However, by making use of quantum mechanical properties this can be improved to the “Heisenberg limit" 1=n, for example by using maximally entangled NOON states [6]. The problem with such an approach is that quantum states are notoriously fragile to particle losses, which typically collapse a state and destroys the phase information. A number of clever schemes have been devised with some robustness to loss which still capture sub-classical precision, but for realistic losses likely to be experienced in an experiment these schemes soon lose their advantage and are beaten by unentangled measurement schemes. A class of states that show the potential for a great improvement over the alternatives are the entangled coherent states (ECSs) [7, 8]. We show that these states allow substantial improvements over unentangled ‘classical’ states and highly-entangled NOON states for a wide range of loss values. We then look at the quantum mechanisms that lead to precise measurements. In optical interferometry multi-mode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false: single mode quantum states perform just as well as their multi-mode entangled counterparts. We go beyond this to show that when photon losses occur- an inevitability in any realistic system - multi-mode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss. These results promote a new way of approaching optical quantum metrology using single-mode states that we expect to have great implications for the future.
 phy5pak@leeds.ac.uk
[1] P. A. Knott, T. J. Proctor, Kae Nemoto, J. A. Dunningham and W. J. Munro, arXiv:1405.7198 (2014).
[2] P. A. Knott, W. J. Munro and J. A. Dunningham, Physical Review A, 89, 053812 (2014).
[3] M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H. Bachor, and W. P. Bowen, Nature Photonics 7, 229 (2013).
[4] J. Aasi et. al., Nature Photonics 7, 613 (2013).
[5] T. P. Purdy, R. W. Peterson and C. A. Regal, Science 339, 801 (2013).
[6] H. Lee, P. Kok, and J. P. Dowling, Journal of Modern Optics 49, 2325 (2002).
[7] C. C. Gerry, Physical Review A 55, 2478 (1997).
[8] J. Joo, W. J. Munro and T. P. Spiller, Physical Review Letters 107, 083601 (2011).

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