Deterministic creation of entangled atom–light Schrödinger-cat states

Abstract

Quantum physics allows for entanglement between microscopic and macroscopic objects, described by discrete and continuous variables, respectively. As in Schrödinger's famous cat gedanken experiment, a box enclosing the objects can keep the entanglement alive. For applications in quantum information processing, however, it is essential to access the objects and manipulate them with suitable quantum tools. Here we reach this goal and deterministically generate entangled light-matter states by reflecting a coherent light pulse with up to four photons on average from an optical cavity containing one atom. The quantum light propagates freely and reaches a remote receiver for quantum state tomography. We produce a plethora of quantum states and observe negative-valued Wigner functions, a characteristic sign of non-classicality. As a first application, we demonstrate a quantum-logic gate between an atom and a light pulse, with the photonic qubit encoded in the phase of the light field.As early as 1935, Schrödinger formulated a gedanken experiment 1 with a living cat and a radioactive atom placed inside a box, which is then closed. When the atom decays, it triggers a death mechanism that kills the cat. According to the laws of quantum physics, the decay of the atom occurs at some random time. Consequently, the time of death of the cat is unknown. Mathematically, the situation inside the box is described by an entangled superposition state that is known as a 'Schrödinger-cat state'. Most remarkable, this state offers a unique access to the atom-cat system, at least in principle. For example, a measurement apparatus that is capable of measuring the atom in a superposition of 'not decayed' and 'decayed' immediately projects the cat into a superposition of 'alive' and 'dead'. Such observation thus transfers the superposition state of the microscopic quantum object into the macroscopic classical world, something weird for a cat. In contrast to the entangled Schrödinger-cat state, the coherent superposition state of the cat is here denoted as a 'cat state'.While notoriously difficult to create 2 , several implementations of Schrödinger-cat states or just cat states have emerged during recent decades. In all these experiments, coherent states with distinguishable phases mimic the two cat states 'dead' and 'alive'. Most prominently, Schrödinger-cat states were explored using a trapped ion 3,4 , with the vibrational state in the trap taking the role of the cat, and coherent microwave fields confined to superconducting boxes were used in combination with Rydberg atoms 5,6 and superconducting qubits 7 . In the latter experiment, the cat state was also released from the microwave resonator 8 .Modern applications in an open quantum-communication and distributed quantum-networking architecture could benefit from cat states that propagate over some distances. As long as superconducting transmission lines exist for short distances only, optical fields propagating through low-loss optical fibres in the (near) visible part of the electrom...

Parity Detection of Propagating Microwave Fields

“…3(c,d). The reconstructed density matrices show a high contrast between the parity of the even and odd cat state, which in other works is referred to as the fringe visibility [7], which we evaluate to V = P even −P odd = 1.7 (1.6 without correction for the readout error) for our data, close to the ideal value of 2. The high-fidelity projection of the detected state into an eigenstate of the parity operator demonstrates the quantum non-demolition nature of the presented parity detection scheme.…”

General superposition states associated to the rotational and inversion symmetries in the phase space

“…1, the Mandel parameter [46] M Q = (∆n) 2 / n is shown for the cyclic Gaussian states of C 2 given in Eq. (18). The figure was made taking into account three different a parameters.…”

“…Instead of that, the low photon cat states, known as kitten states, were generated [16]. After that, the possibility to obtain full cat states has been demonstrated in several studies as: by using the reflexion of a coherent pulse from a optical cavity with one atom [17,18], the use of homodyne detection in a photon number state [19], the photon subtraction from a squeezed vacuum state in a parametric amplifier [20], via ancilla-assisted photon subtraction [21], and by the subtraction of an specific photon number in a squeezed vacuum state [22]. The superposition of coherent states have non-classical features like squeezing of the quadrature components [5,23,24].…”

Visualization of correlations in hybrid discrete—continuous variable quantum systems

“…Recently this has been extended to experiments validating atomic Schrödinger cat states of up to 20 superconducting qubits [32].A case that has not been explored in much detail is the phase-space representation of CV-DV hybridization. This hybridisation is seen in many applications of quantum technologies, including simple gate models for quantum computers, such as hybrid two-qubit gates [33,34], and CV microwave pulse control of DV qubits [35]. The generation of hybrid quantum correlations within CV-DV hybrid 5 systems commonly takes place within the framework of cavity quantum electrodynamics, that describes the interaction between a two-level quantum system and a single mode of a microwave field.…”

“…A hybrid phase-space representation, of all the information within these hybrid systems, is crucial for a more complete understanding of CV-DV hybridization, and its physical properties [42][43][44]. This understanding will be especially helpful for advancing quantum technologies [34,[45][46][47][48], in particular quantum communication where CV-DV hybridization has been used for teleportation [49][50][51] and entanglement distillation [52][53][54].Using the procedure laid out in[24] to generate any quantum state in phase space, and adapting the visualization method from[38], we show how the Wigner function of a hybrid system can be intuitively represented. We begin by presenting examples of important states for CV and DV systems, illustrating how our representation makes correlation information clear.…”