Generating double NOON states of photons in circuit QED

Abstract

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 new type of quantum entangled states, (|N N 00 + |00N N )/ √ 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 + |0, 2N )/ √ 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 ≤ 10 even for the imperfect devices is feasible with the present circuit QED technique.

A high-N00N output of harmonically driven cavity QED

“…Achieving such a big phase estimation number with an ordinary N00N state is far beyond the latest achievements with the current technology which is limited to a few photons. It is notable that our approach of double N00N state generation is different from the one introduced in 33 in principle. In the setup proposed in 33 , N + 2 operational steps is required for generating a double N00N state; however, in our system, we can produce a double N00N state in just a few operational steps, which is independent of the number of the photons, once the initial state is given.…”

“…To appreciate this, let us take , for simplicity. In this case, the generated state reduces to the double N00N state introduced in 33 . Applying the phase shift on the second and the fourth modes of the state, the phase shift of 2 N is accumulated which results in .…”

“…Applying the phase shift on the second and the fourth modes of the state, the phase shift of 2 N is accumulated which results in . This is equivalent to the phase estimation with a N00N state of the form 33 . Considering the fact that number states of more than N = 15 are feasible with the current technology 7,9 , preparing two pairs of N = 15 photons in cavity pairs can result in estimation with a phase resolution .…”

One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED

“…This condition (20) can be readily satisfied by varying g l or |δ l | or both, given |δ 1 |. Note that the detuning |δ l | can be adjusted by changing the frequency of cavity l, and the coupling strength g l can be adjusted by a prior design of the sample with appropriate capacitance or inductance between the qutrit and cavity l [58,59].…”

Creation of superposition of arbitrary states encoded in two high-Q cavities

“…Hence, 3D cavities are good memory elements, which can have coherence time at least four orders of magnitude longer than the transmons. By encoding quantum information in microwave cavities, many schemes have been proposed for synthesizing Bell states [19], NOON states [20][21][22][23][24][25][26], and entangled coherent states [27,28] of multiple cavities, and realizing cross-Kerr nonlinearity interaction between two cavities [29,30].…”