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Register a new userConstructing Qudits from Infinite Dimensional Oscillators by Coupling to Qubits
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An infinite dimensional system such as a quantum harmonic oscillator offers a potentially unbounded Hilbert space for computation, but accessing and manipulating the entire state space requires a physically unrealistic amount of energy. When such a quantum harmonic oscillator is coupled to a qubit, for example via a Jaynes-Cummings interaction, it is well known that the total Hilbert space can be separated into independently accessible subspaces of constant energy, but the number of subspaces is still infinite. Nevertheless, a closed four-dimensional Hilbert space can be analytically constructed from the lowest energy states of the qubit-oscillator system. We extend this idea and show how a $d$-dimensional Hilbert space can be analytically constructed, which is closed under a finite set of unitary operations resulting solely from manipulating standard Jaynes-Cummings Hamiltonian terms. Moreover, we prove that the first-order sideband pulses and carrier pulses comprise a universal set for quantum operations on the qubit-oscillator qudit. This work suggests that the combination of a qubit and a bosonic system may serve as hardware-efficient quantum resources for quantum information processing.
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We investigate the time evolution of entanglement for bipartite systems of arbitrary dimensions under the influence of decoherence. For qubits, we determine the precise entanglement decay rates under different system-environment couplings, including finite temperature effects. For qudits, we show how to obtain upper bounds for the decay rates and also present exact solutions for various classes of states.
We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs, which are examples of molecules with $^2Sigma$ and $^1Sigma$ electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a 4-level qudit. Quantum gates can be implemented using two-photon microwave transitions via levels in a neighboring rotational manifold. We discuss limitations to the usefulness of molecular qudits, arising from off-resonant excitation and decoherence. As an example, we present a protocol for using a molecular qudit of dimension $d=4$ to perform the Deutsch algorithm.
A complex quantum system can be constructed by coupling simple quantum elements to one another. For example, trapped-ion or superconducting quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively quantum objects can be coupled by the exchange of real photons, particularly when driven within resonators that amplify interactions with a single electro-magnetic mode. However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised. Here, we realize phase-coherent interactions between two spatially separated, near-ground-state mechanical oscillators within a driven optical cavity. We observe also the noise imparted by the optical coupling, which results in correlated mechanical fluctuations of the two oscillators. Achieving the quantum backaction dominated regime opens the door to numerous applications of cavity optomechanics with a complex mechanical system. Our results thereby illustrate the potential, and also the challenge, of coupling quantum objects with light.
Photon emission and absorption by an individual qubit are essential elements for the quantum manipulation of light. Here we demonstrate the controllability of spontaneous emission of a qubit in various electromagnetic environments. The parameter regimes that allow for exible control of the qubit emission routes are comprehensively discussed. By properly tuning the system couplings and decay rates, the spontaneous emission rate of the qubit can undergo Purcell enhancement and inhibition. Particularly, when the cavity is prepared in the excited state, the spontaneous emission rate of the qubit can be significantly suppressed. We also demonstrate a spectral filter effect which can be realised by controlling the steady-state emission spectra of qubits.
Generalizations of the classic Bell inequality to higher dimensional quantum systems known as qudits are reputed to exhibit a higher degree of robustness to noise, but such claims are based on one particular noise model. We analyze the violation of the Collins-Gisin-Linden-Massar-Popescu inequality subject to more realistic noise sources and their scaling with dimension. This analysis is inspired by potential Bell inequality experiments with superconducting resonator-based qudits. We find that the robustness of the inequality to noise generally decreases with increasing qudit dimension.
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