We study the contributions of off-resonant transitions to the dynamics of a system of N multi-level atoms sharing one excitation and interacting with the quantized vector electromagnetic field. The rotating wave approximation significantly simplifies the derivation of the equations of motion describing the collective atomic dynamics, but it leads to an incorrect expression for the dispersive part of the atom–atom interaction terms. For the case of two-level atoms and a scalar electromagnetic field, it turns out that the atom–atom interaction can be recovered correctly if integrals over the photon mode frequencies are extended to incorporate negative values. We explicitly derive the atom–atom interaction for multi-level atoms, coupled to the full vector electromagnetic field, and we recover also in this general case the validity of the results obtained by the extension to negative frequencies of the formulas derived with the rotating wave approximation.We study the contributions of off-resonant transitions to the dynamics of a system of N multi-level atoms sharing one excitation and interacting with the quantized vector electromagnetic field. The rotating wave approximation significantly simplifies the derivation of the equations of motion describing the collective atomic dynamics, but it leads to an incorrect expression for the dispersive part of the atom–atom interaction terms. For the case of two-level atoms and a scalar electromagnetic field, it turns out that the atom–atom interaction can be recovered correctly if integrals over the photon mode frequencies are extended to incorporate negative values. We explicitly derive the atom–atom interaction for multi-level atoms, coupled to the full vector electromagnetic field, and we recover also in this general case the validity of the results obtained by the extension to negative frequencies of the formulas derived with the rotating wave approximation.

arXiv:1302.3036Journal of Physics B Atomic Molecular and Optical PhysicsNov 7, 20134 citations

Collective Quantum Feedback of Many-Atom Systems

Sascha Wallentowitz

Acta Physica Hungarica B) Quantum ElectronicsJan 1, 20040 citations

Quasi-integrability and nonlinear resonances in cold atoms under modulation

Rahul Gupta, Manan Jain, Sudhir R. Jain

Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces (PESs): one of them is binding, while the other one is scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents a scenario reminiscent of Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system that is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit systems.Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces (PESs): one of them is binding, while the other one is scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents a scenario reminiscent of Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system that is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit systems.

arXiv:2309.04235Royal Society Open ScienceApr 1, 20240 citations

Gap-Protected Heisenberg-Limited Squeezing with Locally Interacting Multi-Level Spins

Sakshi Bahamnia, Sagar Chaudhary, Arman Duha +1 more

We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local $\mathfrak{su}(D)$ exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling $ξ^2\propto1/N$ in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local $\mathfrak{su}(D)$ exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling $ξ^2\propto1/N$ in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.

quant-pharXiv:2610.02314Oct 5, 20260 citations

Fast and robust two- and three-qubit swapping gates on multi-atomic ensembles in quantum electrodynamic cavity

Sergey N. Andrianov, Sergey A. Moiseev

Creation of quantum computer is outstanding fundamental and practical problem. The quantum computer could be used for execution of very complicated tasks which are not solvable with the classical computers. The first prototype of solid state quantum computer was created in 2009 with superconducting qubits. However, it suffers from the decoherent processes and it is desirable to find more practical encoding of qubits with long-lived coherence. It could be single impurity or vacancy centers in solids, but their interaction with electromagnetic radiation is rather weak. So, here, ensembles of atoms were proposed for the qubit encoding by using the dipole blockade mechanism in order to turn multilevel systems in two level ones. But dipole-dipole based blockade introduces an additional decoherence that limits its practical significance. Recently, the collective blockade mechanism has been proposed for the system of three-level atoms by using the different frequency shifts for the Raman transitions between the collective atomic states characterized by a different number of the excited atoms. Here, we propose two qubit gate by using another collective blockade mechanism in the system of two level atoms based on exchange interaction via the virtual photons between the multi-atomic ensembles in the resonator. Also we demonstrate the possibility of three qubit gate (Controlled SWAP gate) using a suppression of the swap-process between two multi-atomic ensembles due to dynamical shift of the atomic levels controlled by the states of photon encoded qubit.Creation of quantum computer is outstanding fundamental and practical problem. The quantum computer could be used for execution of very complicated tasks which are not solvable with the classical computers. The first prototype of solid state quantum computer was created in 2009 with superconducting qubits. However, it suffers from the decoherent processes and it is desirable to find more practical encoding of qubits with long-lived coherence. It could be single impurity or vacancy centers in solids, but their interaction with electromagnetic radiation is rather weak. So, here, ensembles of atoms were proposed for the qubit encoding by using the dipole blockade mechanism in order to turn multilevel systems in two level ones. But dipole-dipole based blockade introduces an additional decoherence that limits its practical significance. Recently, the collective blockade mechanism has been proposed for the system of three-level atoms by using the different frequency shifts for the Raman transitions between the collective atomic states characterized by a different number of the excited atoms. Here, we propose two qubit gate by using another collective blockade mechanism in the system of two level atoms based on exchange interaction via the virtual photons between the multi-atomic ensembles in the resonator. Also we demonstrate the possibility of three qubit gate (Controlled SWAP gate) using a suppression of the swap-process between two multi-atomic ensembles due to dynamical shift of the atomic levels controlled by the states of photon encoded qubit.

arXiv:1103.3098Mar 16, 20114 citations

\mathfrak{su}(D)

exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling

ξ^2\propto1/N

in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.