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Science

High-NOON States by Mixing Quantum and Classical Light

I. Afek, O. Ambar, Yaron R. Silberberg

Published May 13, 2010• 621 citations
Publisher

Abstract

All and Nothing Entanglement, where a system can be in a superposition of a number of distinct states simultaneously, is a principle at the foundation of quantum mechanics (recall Schrödinger's cat, which is both dead and alive). It can also be used in many applications—imaging, communication, patterning, and metrology—with the effect being amplified by entangling larger systems. However, the systematic generation of “large” entangled systems is challenging. Afek et al. (p. 879 ; see the Perspective by Wildfeuer ) present a technique for generating many-photon entanglement in so-called NOON states, where there are two possible paths and N photons in one path and 0 in the other—the system being a superposition of “all and nothing” states. Mixing of entangled pairs with classical light at a beam splitter formed up to five photon-entangled states. The technique should be generally applicable to generate higher-order entangled states.

DOI
10.1126/science.1188172

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To generate a NOON state with a large photon number $N$, the number of operational steps could be large and the fidelity will decrease rapidly with $N$. Here we propose a method to generate a type of quantum entangled states, $(|NN00\ensuremath{\rangle}+|00NN\ensuremath{\rangle})/\sqrt{2}$, called ``double NOON'' states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the ``double'' NOON state creation needs only $N+2$ operational steps. One application of double NOON states is to get a phase error of $1/(2N)$ in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $(|2N,0\ensuremath{\rangle}+|0,2N\ensuremath{\rangle})/\sqrt{2}$ is needed, which requires at least $2N$ operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\ensuremath{\le}10$ even for imperfect devices is feasible with the present circuit QED technique.

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All and Nothing Entanglement, where a system can be in a superposition of a number of distinct states simultaneously, is a principle at the foundation of quantum mechanics (recall Schrödinger's cat, which is both dead and alive). It can also be used in many applications—imaging, communication, patterning, and metrology—with the effect being amplified by entangling larger systems. However, the systematic generation of “large” entangled systems is challenging. Afek et al. (p. 879 ; see the Perspective by Wildfeuer ) present a technique for generating many-photon entanglement in so-called NOON states, where there are two possible paths and N photons in one path and 0 in the other—the system being a superposition of “all and nothing” states. Mixing of entangled pairs with classical light at a beam splitter formed up to five photon-entangled states. The technique should be generally applicable to generate higher-order entangled states.
"Schrodinger's cat" is a gedankenexperiment intended to highlight conceptual difficulties in the interpretation of quantum mechanics. The generation of 'cat-like' states is central to numerous quantum information protocols. In particular, much attention has been drawn by states containing N photons in a superposition of all being in one of two designated modes. These maximally path entangled states, known as 'NOON' states, exhibit enhanced phase sensitivity and allow reaching the fundamental quantum limit of precision measurement. Such states could also be used for obtaining 'super-resolution' in quantum lithography. Creation of NOON states in the lab, has been limited to N=3. Surpassing this has proven a formidable experimental challenge. Here, we realize a scheme for generation of high fidelity NOON states with arbitrarily large N. We demonstrate the versatility of the scheme by measuring up to N=5 in a single setup, this is in contrast to previous experiments which were custom-designed for a specific N. The scheme is based on high order interference between 'quantum' down-converted light and 'classical' coherent light in the photon number basis. Our results verify the high degree of path entanglement which emerges naturally from the interference of two ubiquitous, easy to generate, states of light.
To generate a NOON state with a large photon number NNN, the number of operational steps could be large and the fidelity will decrease rapidly with NNN. Here we propose a method to generate a type of quantum entangled states, $(|NN00\ensuremath{\rangle}+|00NN\ensuremath{\rangle})/\sqrt{2}$, called ``double NOON'' states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the ``double'' NOON state creation needs only N+2N+2N+2 operational steps. One application of double NOON states is to get a phase error of 1/(2N)1/(2N)1/(2N) in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $(|2N,0\ensuremath{\rangle}+|0,2N\ensuremath{\rangle})/\sqrt{2}$ is needed, which requires at least 2N2N2N operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\ensuremath{\le}10$ even for imperfect devices is feasible with the present circuit QED technique.
Quantum entanglement is a fascinating physical resource that is central to the field of quantum information processing with important applications in such areas as quantum computing, quantum communication, quantum metrology, and quantum imaging. \nIt describes the physical phenomenon in which the quantum state of a multipartite system cannot be written as consisting of constituents that are independent of each other. In this case, the state of the system is called an entangled state. In this \ndissertation, the entanglement of photons--the elementary excitations of the quantized electromagnetic field--is studied. A focus is made on a particular type of entangled states of light called the d-mode N-photon NOON state, which consists of N photons with the N photons as an ensemble appearing at d orthogonal modes simultaneously and are inseparable. \nIn quantum metrology, a field that investigates the ultimate precision of measurements of unknown physical parameters, the two-mode NOON state has been studied extensively with respect to its ability to achieve super-resolution and super-sensitivity in the estimation of a single parameter. A lot of theoretical research has been conducted on the generation of two-mode NOON states, and two-mode NOON states with up to 4 photons have been experimentally and efficiently produced. On the other hand, recently there has been increasing interest in the study of the simultaneous estimation of multiple parameters. Accordingly, the multi-mode NOON state has been attracting more and more attention in view of its potential for enhanced efficiency as compared to using multiple two-mode NOON states separately to estimate the parameters. Nevertheless, no known generation method of multi-mode NOON states with more than 2 photons or 2 modes exists so far. \nIn this dissertation, several scalable generation methods of multi-mode NOON states are proposed. These methods take advantage of multi-photon quantum interference and they can theoretically be applied to produce NOON states with an \narbitrary number of modes and an arbitrary number of photons. The intrinsic generation probability for each method is calculated, and the methods are compared in regards to their feasibility and efficiency. The advantages of using multi-mode NOON \nstates in quantum metrology are also analyzed and discussed in detail.
In quantum theory, a particle is allowed to be in a state of coherent superposition among a set of orthogonal states. A vivid picture of this concept is the “Schrödinger cat”: a cat is alive and dead simultaneously. This would be no surprise if one means a large number of an ensemble of cats with 50% alive and 50% dead. But, “Schrödinger cat” is a cat. People are talking about a cat being alive and dead simultaneously. In mathematics, the best word to characterize the relationship between states “alive” and “dead” is perhaps “orthogonal”. In quantum mechanics, the superposition of orthogonal states is used to describe the state of a quantum object, or a particle. The superposition principle is indeed a mystery compared to our everyday classical life experience. Beyond the superposition of orthogonal single-particle states, the superposition of orthogonal multi-particle states represents an even more troubling concept in classical theory.
We propose a bootstrapping approach to generation of maximally path-entangled states of photons, so called ``NOON states'', achievable within the current experimental technology. Strong atom-light interaction of cavity QED can be employed to generate NOON states with about 100 photons; which can then be used to boost the existing experimental Kerr nonlinearities based on quantum coherence effects to facilitate NOON generation with arbitrarily large number of photons. We also offer an alternative scheme that uses an atom-cavity dispersive interaction to obtain sufficiently high Kerr-nonlinearity necessary for arbitrary NOON generation.
We propose a bootstrapping approach to the generation of maximally path-entangled states of photons, so-called "NOON states." The strong atom-light interaction of cavity QED can be employed to generate NOON states with about 100 photons. These can then be used to boost the existing experimental Kerr nonlinearities based on quantum coherence effects, to facilitate NOON generation with an arbitrarily large number of photons. We also offer an alternative scheme that uses an atom-cavity dispersive interaction to obtain a sufficiently high Kerr nonlinearity necessary for arbitrary NOON generation.