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arXiv:2207.04617 · Physical Review A

Experimental preparation of generalized cat states for itinerant microwave photons

Zenghui Bao, Zhiling Wang, Yukai Wu, Yan Li, Weizhou Cai, Weiting Wang, Yuwei Ma, Tianqi Cai, Xiyue Han, Jiahui Wang, Yipu Song, Luyan Sun, Hongyi Zhang, Luming Duan

Published Jun 21, 2022• 11 citations
arXivHTMLPDF

Abstract

Generalized cat states represent arbitrary superpositions of coherent states, which are of great importance in various quantum information processing protocols. Here we demonstrate a versatile approach to creating generalized itinerant cat states in the microwave domain, by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We show that with a coherent control of the qubit state, a full control over the coherent-state superposition can be realized. The prepared cat states are verified through quantum state tomography of the qubit-state-dependent reflection photon field. We further quantify quantum coherence in the prepared cat states based on the resource theory, revealing a good experimental control on the coherent-state superpositions. The photon number statistic and the squeezing properties are also analyzed. Remarkably, fourth-order squeezing is observed in the experimental states. Those results open up new possibilities of applying generalized cat states for the purpose of quantum information processing.

DOI
10.1103/physreva.105.063717

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Generalized cat states represent arbitrary superpositions of coherent states, which are of great importance in various quantum information processing protocols. Here we demonstrate a versatile approach to creating generalized itinerant cat states in the microwave domain, by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We show that with a coherent control of the qubit state, a full control over the coherent-state superposition can be realized. The prepared cat states are verified through quantum state tomography of the qubit-state-dependent reflection photon field. We further quantify quantum coherence in the prepared cat states based on the resource theory, revealing a good experimental control on the coherent-state superpositions. The photon number statistic and the squeezing properties are also analyzed. Remarkably, fourth-order squeezing is observed in the experimental states. Those results open up new possibilities of applying generalized cat states for the purpose of quantum information processing.
Schrödinger's cat originates from the famous thought experiment querying the counterintuitive quantum superposition of macroscopic objects. As a natural extension, several "cats" (quasi-classical objects) can be prepared into coherent quantum superposition states, which is known as multipartite cat states demonstrating quantum entanglement among macroscopically distinct objects. Here, we present a highly scalable approach to deterministically create flying multipartite Schrödinger's cat states by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We perform full quantum state tomography on the cat states with up to four photonic modes and confirm the existence of quantum entanglement among them. We also witness the hybrid entanglement between discrete-variable states (the qubit) and continuous-variable states (the flying multipartite cat) through a joint quantum state tomography. Our work provides an enabling step for implementing a series of quantum metrology and quantum information processing protocols based on cat states.
A cat-state is a superposition of two coherent states with amplitudes α0α_{0}α0​ and −α0-α_{0}−α0​. Recent experiments create cat states in a microwave cavity field using superconducting circuits. As with degenerate parametric oscillation (DPO) in an adiabatic and highly nonlinear limit, the states are formed in a signal cavity mode via a two-photon dissipative process induced by the down conversion of a pump field to generate pairs of signal photons. The damping of the signal and the presence of thermal fluctuations rapidly decoheres the state, and the effect on the dynamics is to either destroy the possibility of a cat state, or else to sharply reduce the lifetime and size of the cat-states that can be formed. In this paper, we study the effect on both the DPO and microwave systems of a squeezed reservoir coupled to the cavity. While the threshold nonlinearity is not altered, we show that the use of squeezed states significantly lengthens the lifetime of the cat states. This improves the feasibility of generating cat states of large amplitude and with a greater degree of quantum macroscopic coherence, which is necessary for many quantum technology applications. Using current experimental parameters for the microwave set-up, which requires a modified Hamiltonian, we further demonstrate how squeezed states enhance the quality of the cat states that could be formed in this regime. Squeezing also combats the significant decoherence due to thermal noise, which is relevant for microwave fields at finite temperature. By modeling a thermal squeezed reservoir, we show that the thermal decoherence of the dynamical cat states can be inhibited by a careful control of the squeezing of the reservoir. To signify the quality of the cat state, we consider different signatures including fringes and negativity, and the Cl1C_{l_{1}}Cl1​​ measure of quantum coherence.
In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control by using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a tool set of conditional qubit-photon logic, we mapped an arbitrary qubit state to a superposition of coherent states, known as a "cat state." We created cat states as large as 111 photons and extended this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.
Quantum superpositions of distinct coherent states in a single-mode harmonic oscillator, known as "cat states," have been an elegant demonstration of Schrödinger's famous cat paradox. Here, we realize a two-mode cat state of electromagnetic fields in two microwave cavities bridged by a superconducting artificial atom, which can also be viewed as an entangled pair of single-cavity cat states. We present full quantum state tomography of this complex cat state over a Hilbert space exceeding 100 dimensions via quantum nondemolition measurements of the joint photon number parity. The ability to manipulate such multicavity quantum states paves the way for logical operations between redundantly encoded qubits for fault-tolerant quantum computation and communication.
The latest breakthroughs in microwave quantum photonics in superconducting circuits are presented. Advancing technologies of Josephson junction quantum bits (qubits) have been applied to control and measurement of itinerant microwave fields. Methods to generate nonclassical microwave states such as single-photon states and squeezed states have been developed. Techniques to characterize those nonclassical itinerant states have also been established. They are ready to be combined to demonstrate various quantum protocols, which extend the possibilities of quantum information processing, quantum metrology, and quantum communications using superconducting circuits.
A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the quantum state of itinerant single photon Fock states and their superposition with the vacuum by analyzing moments of the measured amplitude distribution up to fourth order. Using linear amplifiers and quadrature amplitude detectors, we have developed efficient methods to separate the detected single photon signal from the noise added by the amplifier. From our measurement data we have also reconstructed the corresponding Wigner function.