Christoph F. Wildfeuer

Entangled Fock states for robust quantum optical metrology, imaging, and sensing

We propose a class of path-entangled photon Fock states for robust quantum optical metrology, imaging, and sensing in the presence of loss. We model propagation loss with beam splitters and derive a reduced densitymatrix formalism from which we examine how photon loss affects coherence. It is shown that particular entangled number states, which contain a special superposition of photons in both arms of a Mach-Zehnder interferometer, are resilient to environmental decoherence. We demonstrate an order of magnitude greater visibility with loss than possible with path-entangled N ,0 + 0, N states. We also show that the effectiveness of a detection scheme is related to super-resolution visibility.

Optimization of quantum interferometric metrological sensors in the presence of photon loss

We optimize two-mode entangled number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number. We optimize to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss, the optimal state is the maximally path-entangled so-called N00N state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss, the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss, with applications to quantum imaging, metrology, sensing, and information processing.

Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors

There has been much recent interest in quantum optical interferometry for applications to metrology, subwavelength imaging, and remote sensing such as in quantum laser radar (LADAR). For quantum LADAR, atmospheric absorption rapidly degrades any quantum state of light, so that for high-photon loss the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the Beer law for classical optical attenuation, and which provides sensitivity at the shot-noise limit. We show that coherent light coupled with photon-number-resolving detectors can provide a super-resolution much below the Rayleigh diffraction limit, with sensitivity no worse than shot noise in terms of the detected photon power.

Near-space flight of a correlated photon system

We report the successful test flight of a device for generating and monitoring correlated photon pairs under near-space conditions up to 35.5 km altitude. Data from ground based qualification tests and the high altitude experiment demonstrate that the device continues to operate even under harsh environmental conditions. The design of the rugged, compact and power-efficient photon pair system is presented. This design enables autonomous photon pair systems to be deployed on low-resource platforms such as nanosatellites hosting remote nodes of a quantum key distribution network. These results pave the way for tests of entangled photon technology in low earth orbit.

Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector

With photon-number resolving detectors, we show compression of interference fringes with increasing photon numbers for a Fabry-Perot interferometer. This feature provides a higher precision in determining the position of the interference maxima compared to a classical detection strategy. We also theoretically show supersensitivity if N-photon states are sent into the interferometer and a photon-number resolving measurement is performed.

Strong violations of bell-type inequalities for path-entangled number states

We show that nonlocal correlation experiments on the two spatially separated modes of a maximally path-entangled number state may be performed. They lead to a violation of a Clauser-Horne Bell inequality for any finite photon number N. We also present an analytical expression for the two-mode Wigner function of a maximally path-entangled number state and investigate a Clauser-Horne-Shimony-Holt Bell inequality for such a state. We test other Bell-type inequalities. Some are violated by a constant amount for any N.

Enhancing Image Contrast Using Coherent States and Photon Number Resolving Detectors

We experimentally map the transverse profile of diffractionlimited beams using photon-number-resolving detectors.We observe strong compression of diffracted beam profiles for high detected photon number. This effect leads to higher contrast than a conventional irradiance profile between two Airy disk-beams separated by the Rayleigh criterion.

The information of high-dimensional time-bin encoded photons

Abstract High-dimensional entanglement is an important physical resource for quantum communication. A basic issue for any communication scheme is how many shared bits two parties can extract subject to experimental noise. We determine the shared information that can be extracted from time-bin entangled photons using frame encoding. We consider photons generated by a general down-conversion source and also model losses, dark counts and the effects of multiple photons within each frame. Furthermore, we describe a procedure for including other imperfections such as after-pulsing, detector dead-times and jitter. The results are illustrated by deriving analytic expressions for the maximum information that can be extracted from high-dimensional time-bin entangled photons generated by down conversion. A key finding is that under realistic conditions and using standard SPAD detectors one can still choose the frame size so as to extract over 10 bits per photon. These results are thus useful for experiments on high-dimensional quantum-key distribution systems, but are not limited to such systems. For example, the results are also useful for determining the limits of fibre arrays or within time-multiplexing schemes. Graphical abstract

Optimizing the multiphoton absorption properties of maximally path-entangled number states

In this paper we examine the N-photon absorption properties of maximally path-entangled number states (N00N states). We consider two cases. The first involves the N-photon absorption properties of the ideal N00N state, one that does not include spectral information. We study how the N-photon absorption probability of this state scales with N, confirming results presented by others in a previous paper by a different method. We compare this to the absorption probability of various other states. The second case is that of two-photon absorption for an N=2 N00N state generated from a type-II spontaneous down-conversion event. In this situation we find that the absorption probability is both better than analogous coherent light (due to frequency entanglement) and highly dependent on the optical setup. We show that the poor production rates of quantum states of light may be partially mitigated by adjusting the spectral parameters to improve their two-photon absorption rates. This work has application to quantum imaging, particularly quantum lithography, where the N-photon absorbing process in the lithographic resist must be optimized for practical applications.

Managing Multistate Quantum Entanglement

A general route for creating entangled states of large numbers of photons may be relevant to other applications of interferometry, such as gravity wave detection. Good experiments minimally perturb the sample under study, but in the quantum realm, measurement cannot be separated from the system. Before the measurement, all possible outcomes can form an entangled state; measurement then causes this entangled state to collapse to one outcome. In 1935, Schrödinger presented a thought experiment to show how strange this situation really is. A cat is hidden in a box along with a sample of radioactive nuclei. If a nuclear decay occurs, poison is released and the poor cat dies. However, until we look in the box, the state of the cat entangles both a live and a dead cat. Experiments with Schrödinger-cat states that entangle several particles continue to provide deep insights into the measurement process. One such state, called a NOON state, entangles a fixed number of photons N, all of which are in one of two possible states (if these were coins, they would be all heads or all tails). On page 879 of this issue, Afek et al. (1) achieved a record by making NOON states in an interferometer with five entangled photons. Their approach may have implications for other implementations of interferometry, such as gravity wave detectors.