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.
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.
We propose a novel scheme for the efficient production of entangled states for N photons of the form |N>(a)|0>(b) + |0>(a)|N>(b) (NOON states) based on the resonant interaction of a pair of quantized cavity modes with an ensemble of atoms. We show that, in the strong-coupling regime, the adiabatic evolution of the system tends to a limiting state that describes mesoscopic entanglement between photons and atoms which can easily be converted to a purely photonic or atomic NOON state. We also demonstrate the remarkable property that the efficiency of this scheme increases exponentially with the cavity cooperativity factor, which gives efficient access to high number NOON states. The experimental feasibility of the scheme is discussed, and its efficiency is demonstrated numerically.
Path-entangled
N-photon systems described by NOON states are the main ingredient of many quantum information and quantum imaging protocols. Our analysis aims to lead the way toward the implementation of both NOON-state sources and their applications. To this end, we study the functionality of ``real'' NOON-state sources by quantifying the effect real experimental apparatuses have on the actual generation of the desired NOON state. In particular, since the conditional generation of NOON states strongly relies on photon counters, we evaluate the dependence of both the reliability and the signal-to-noise ratio of ``real'' NOON-state sources on detection losses. We find a surprising result: NOON-state sources relying on nondetection are much more reliable than NOON-state sources relying on single-photon detection. Also the comparison of the resources required to implement these two protocols comes out to be in favor of NOON-state sources based on nondetection. A scheme to improve the performances of ``real'' NOON-state sources based on single-photon detection is also proposed and analyzed.
"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.