Abstract
A Hamiltonian is presented, which can be used to convert any asymmetric state $|\varphi \rangle_{a}|\phi \rangle_{b}$ of two oscillators $a$ and $b$ into an entangled state. Furthermore, with this Hamiltonian and local operations only, two oscillators, initially in any asymmetric initial states, can be entangled with a third oscillator. The prepared entangled states can be engineered with an arbitrary degree of entanglement. A discussion on the realization of this Hamiltonian is given. Numerical simulations show that, with current circuit QED technology, it is feasible to generate high-fidelity entangled states of two microwave optical fields, such as entangled coherent states, entangled squeezed states, entangled coherent-squeezed states, and entangled cat states. Our finding opens a new avenue for creating not only two-color or three-color entanglement of light but also wave-like or particle-like entanglement or novel wave-like and particle-like hybrid entanglement.
Highlights
Entangled states of light are a fundamental resource for many quantum information tasks [1,2,3,4,5,6,7,8]
In the regime of continuous variables, EPR states of light have been experimentally generated from two independent squeezed fields [11,12], two independent coherent fields [13], or a single squeezed light source [14]; two- or three-color entangled states of light have been experimentally prepared by means of non-degenerate optical parametric oscillators [15,16,17]
Hybrid entanglement between particlelike and wave-like optical qubits or between quantum and classical states of light [18,19] has been demonstrated in experiments, which has drawn increasing attention because hybrid entanglement of light is a key resource in establishing hybrid quantum networks and connecting quantum processors with different encoding qubits
Summary
Entangled states of light are a fundamental resource for many quantum information tasks [1,2,3,4,5,6,7,8]. Note that Eq (1) is different from the well-known Hamiltonian H = ω a†a + ˆb†ˆb + λ a†ˆb + aˆb† describing two single-mode interacting oscillators This is because each term in Eq (1) contains a coupler operator. A strong anharmonicity (e.g., a superconducting flux device) This condition can be satisfied by adjusting the coupler level spacings or the resonator frequencies. It is noted that based on the Hamiltonian (1), when the coupler is in the state |g , a SWAP gate of two discrete-variable qubits or two continuous-variable qubits, defined by |φ a |φ b → |φ a |φ b , |φ a |φ b → |φ a |φ b , |φ a |φ b → |φ a |φ b , and |φ a |φ b → |φ a |φ b , can be realized via a single operation.
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