We investigate the generation of entanglement between the axial degrees of freedom of electrons confined in separated locations in planar Penning traps. We show that there are two different sources of entanglement: one is related with the mechanism of switching on and off the electrical coupling between the two electrons, and the other is due to the two-quanta-transition term of the coupling interaction. We show that the degree of entanglement can be controlled by adjusting the strength of the coupling between the traps and the time of interaction. We show that the coupled electrons behave as a temporal active interferometer.
We investigate the generation of entanglement between the axial degrees of freedom of electrons confined in separated locations in planar Penning traps. We show that there are two different sources of entanglement: one is related with the mechanism of switching on and off the electrical coupling between the two electrons, and the other is due to the two-quanta-transition term of the coupling interaction. We show that the degree of entanglement can be controlled by adjusting the strength of the coupling between the traps and the time of interaction. We show that the coupled electrons behave as a temporal active interferometer.
Recent studies have shown that linear electron optics can be used to generate entangled two-particle states from nonentangled ones if additional measurements of charge or parity are performed. We have investigated such nondeterministic entanglement production in electronic versions of the Mach-Zehnder interferometer, where spin-dependent interference occurs due to the presence of electric-field tunable Rashba spin splitting. Adjustment of the spin-precession length turns out to switch the entangler on and off, as well as control the detailed form of entangled output states.
Two electrons in planar Penning traps can be coupled by connecting the trap electrodes with a metallic wire. The wire provides a capacitive and resistive link between the image charges that the electron oscillation (axial motion) is inducing in the electrodes. This can be operated as a quantum network to transfer excitation quanta between the traps and to entangle the two electrons. We give a detailed analysis of this system in the dispersive limit and assess the impact of resistive thermal noise. The latter is found to be remarkably small at temperatures below 4 K in miniaturized planar traps (sizes below 1 mm). The master equation for the two-electron system in the presence of resistive noise is solved exactly. We compute fidelities for basic quantum gates needed in quantum information processing.
A one-electron qubit would offer a new option for quantum information science, including the possibility of extremely long coherence times. One-quantum cyclotron transitions and spin flips have been observed for a single electron in a cylindrical Penning trap. However, an electron suspended in a planar Penning trap is a more promising building block for the array of coupled qubits needed for quantum information studies. The optimized design configurations identified here promise to make it possible to realize the elusive goal of one trapped electron in a planar Penning trap---a substantial step toward a one-electron qubit.
Quantum computers have the potential to solve problems far beyond the reach of classical computers by using the principles of superposition and entanglement. However, existing platforms face challenges such as short coherence times, interference from the environment, and difficulties in scaling up.Trapped electrons in a planar Penning trap offer a promising alternative. Unlike other qubits, electrons do not interact with nuclear spins, which helps maintain quantum states for much longer. Additionally, their strong confinement allows for fast and precise quantum operations. In our approach, electron spins serve as logical qubits, while their motional states are used for entanglement. Our setup consists of 2-dimensional array of micro-sized Penning traps fabricated on a ceramic chip, placed inside a 1T superconducting magnet and cooled in a dilution refrigerator to reach millikelvin temperatures. This extreme cooling reduces unwanted motion and makes it possible to entangle electron spins and perform quantum gates with high accuracy. At Inter-University Accelerator Centre (IUAC), New Delhi, India, we are developing a prototype planar Penning trap. This new system offers a stable, scalable, and high-coherence platform for quantum computing.
Using a method of characterizing entanglement in the framework of quantum field theory, we investigate the optical generation and quantitative characterizations of quantum entanglement in an electron-hole system, in presence of spin-orbit coupling, and especially make a theoretical analysis of a recent experimental result. Basically, such entanglement should be considered as between occupation numbers of single-particle basis states, and is essentially generated by coupling between different single-particle basis states in the second-quantized Hamiltonian. Interaction with two resonant light modes of different circular polarizations generically leads to a superposition of ground state and two heavy-hole excitonic states. When and only when the state is a superposition of only the two excitonic eigenstates, the entanglement reduces to that between two distinguishable particles, each with two degrees of freedom, namely, band index, as characterized by angular momentum, and orbit, as characterized by position or momentum. The band-index state, obtained by tracing over the orbital degree of freedom, is found to be a pure state, hence the band index and orbital degrees of freedom are separated in this state. We propose some basic ideas on spatially separating the electron and the hole, so that the entanglement of band indices, or angular momenta, is between spatially separated electron and hole.
Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin degrees of freedom are encoded in low-lying electronic levels, and interactions among the spins are mediated through crystal vibrations. Here we propose a new approach which enables the quantum simulation of two-dimensional spin systems with interaction strengths that are increased by orders of magnitude. This, together with the unprecedented longevity of trapped ions, opens an avenue for the exploration of phenomena that take place on long timescales, e.g., slow and collective relaxation in frustrated and kinetically constrained systems. Our platform makes use of the strong dipolar interactions among electronic Rydberg states and planar confinement provided by a Penning trap. We investigate how the strong electric and magnetic fields that form this trap affect the properties of the Rydberg states and show that spin-spin interaction strengths on the order of MHz are achievable under experimentally realistic conditions. As a brief illustration of the capabilities of this quantum simulator, we study the entanglement in a frustrated spin system realized by three ions.