Spin ensembles play a pivotal role in various quantum applications such as metrology and simulations of many-body physics. Recent research has proposed utilizing spin cat states to encode logical quantum information, with logical lifetimes potentially on the order of seconds, achieved via enhanced collective interactions that scale with system size. We investigate the dynamics of spin cat states under inhomogeneous broadening, revealing a phenomenon termed ``parity-sensitive inhomogeneous dephasing'': For small amplitudes, odd cat states are significantly more susceptible to inhomogeneous dephasing than even cat states due to the difference in parity symmetry. This discrepancy between even and odd cat states vanishes at large amplitudes and behaves similarly to a spin coherent state with the same amplitude. To analyze the stability of the spin coherent state, we perform a mean-field analysis of the driven-dissipative dynamics, from which we identify a synchronization phase transition wherein the ensemble becomes completely dephased beyond a critical inhomogeneous linewidth. The mean-field analysis suggests that the dissipative stabilization can suppress the decoherence effects from inhomogeneous broadening. We argue that the stability of the mean-field model provides a reasonable estimate for that of spin cat states with a large amplitude in the full quantum model. Our findings shed light on the stability of collective spin states, which is important for advancing quantum technologies.
Spin ensembles play a pivotal role in various quantum applications such as metrology and simulations of many-body physics. Recent research has proposed utilizing spin cat states to encode logical quantum information, with logical lifetimes potentially on the order of seconds, achieved via enhanced collective interactions that scale with system size. We investigate the dynamics of spin cat states under inhomogeneous broadening, revealing a phenomenon termed ``parity-sensitive inhomogeneous dephasing'': For small amplitudes, odd cat states are significantly more susceptible to inhomogeneous dephasing than even cat states due to the difference in parity symmetry. This discrepancy between even and odd cat states vanishes at large amplitudes and behaves similarly to a spin coherent state with the same amplitude. To analyze the stability of the spin coherent state, we perform a mean-field analysis of the driven-dissipative dynamics, from which we identify a synchronization phase transition wherein the ensemble becomes completely dephased beyond a critical inhomogeneous linewidth. The mean-field analysis suggests that the dissipative stabilization can suppress the decoherence effects from inhomogeneous broadening. We argue that the stability of the mean-field model provides a reasonable estimate for that of spin cat states with a large amplitude in the full quantum model. Our findings shed light on the stability of collective spin states, which is important for advancing quantum technologies.
The enhanced collective coupling to weak quantum fields may turn atomic or spin ensembles into an important component in quantum information processing architectures. Inhomogeneous broadening can, however, significantly reduce the coupling and the lifetime of the collective excitation that represent the quantum information. In this paper we show that the width and shape of the inhomogeneous broadening have a striking influence on the dynamics of the cavity-ensemble system and may lead to narrowing of the linewidth of the collective states. We underpin our findings with the examples of a Gaussian and a Lorentzian profile of the inhomogeneity.
We propose using even and odd Schödinger cat states formed from coherent states of U(3) of an ensemble of qutrits with a symmetrical V-configuration (a qubit-disguised qutrit) to encode a logical qubit. These carefully engineered logical qubit states are parameter independent stationary states of the effective master equation governing the evolution of the ensemble and, consequently, constitute dark states and are invulnerable to dissipation and correlated collective dephasing. In particular, the logical qubit states are immune to single qutrit decay (the analogous of single photon loss process for qutrits) and simultaneous decay and driving of two qutrits (the analogous two-photon loss and driving processes for qutrits). In addition, we show how to implement the single-qubit quantum NOT gate and the Hadamard gate followed by either the phase gate or the phase and Z gates. We study analytically the case of two qutrits and conclude that the logical qubit states exhibit parity-sensitive inhomogeneous broadening and local correlated dephasing: the even logical state is completely immune to these processes, while odd one is vulnerable. Nevertheless, in the presence of these interactions one can also define another odd state with mixed permutation symmetry that is immune to both inhomogeneous broadening and local correlated dephasing. We suggest that these results can be extrapolated to an arbitrary number of qutrits. The effective master equation is deduced from a physical system composed of two parametrically coupled cavities with one of them interacting dispersively with an ensemble of three-level atoms (the qutrits). In principle this physical system can be implemented by means of two coplanar waveguide resonators, a SQUID parametrically coupling them, and a cloud of alkali atoms close to one of the resonators.
Quantum error correction (QEC) is indispensable for scalable quantum computing, but implementing it with minimal hardware overhead remains a central challenge. Large spin systems with collective degrees of freedom offer a promising route to reducing the control complexity of qubit architectures while retaining a large Hilbert space for fault-tolerant encoding. However, existing proposals for logical gates and QEC in spin ensembles generally rely on inefficient higher-order interactions. Here we introduce spin-N-Cat codes, which encode logical qubits in superpositions of spin-coherent states and generalize bosonic Cat codes to the modular subspaces of permutationally symmetric spin ensembles. The code corrects collective and individual dephasing, excitation, and decay errors. We also present an efficient physical realization in central-spin systems, such as a quantum dot, where encoding, decoding, and a universal, fault-tolerant, and bias-preserving gate set are implemented using only first-order interactions. Numerical simulations demonstrate high logical fidelity under dephasing and excitation-decay noise, independent of noise bias, and that full QEC cycles are feasible with realistic microscopic parameters. For the large collective spins available in quantum dots, this translates into a substantial extension of coherence time. Our results establish spin-N-Cat codes as a scalable, hardware-efficient approach to QEC in spin-based quantum architectures.
Abstract We investigate the performance of inhomogeneously broadened spin ensembles as quantum memories under continuous dynamical decoupling. The role of the continuous driving field is twofold: firstly, it decouples individual spins from magnetic noise; secondly, and more importantly, it suppresses and reshapes the spectral inhomogeneity of spin ensembles. We show that a continuous driving field, which itself may also be inhomogeneous over the ensemble, can considerably enhance the decay of the tails of the inhomogeneous broadening distribution. This fact enables a spin-ensemble-based quantum memory to exploit the effect of cavity protection and achieve a much longer storage time. In particular, for a spin ensemble with a Lorentzian spectral distribution, our calculations demonstrate that continuous dynamical decoupling has the potential to improve its storage time by orders of magnitude for the state-of-the-art experimental parameters.
This thesis explores the effects of decoherence and dephasing on single- and many- body dynamics of spin-systems. A particular realisation of the spin systems that the work focuses on are highly excited, Rydberg states of atoms. A software library ARC (Alkali Rydberg Calculator) for calculating properties of Rydberg states in alkali metals is presented, with particular attention to the multi- atom and multi-level effects that influence many-body dynamics in realistic systems, and properties related to terahertz imaging with alkali atom Rydberg states. Dressed-state electromagnetically induced transparency (EIT) is proposed as a way of preparing uniform-phase spin-waves in ladder excitation schemes, making the collective excitation storage insensitive to motional dephasing. Proof of concept dressed state EIT experiments are presented. Strong resonant dressing is also theoretically analysed as a way of preparing velocity superposition of spin-waves. The developed theoretical model is in a good agreement with existing experimental data on single-photon many-atom quantum beats in diamond excitation schemes. By modelling the strongly driven Rydberg ensembles, many-body dynamics of driven-dissipative spin systems is analysed. Working in the limit of strong dephasing, the effects of fluctuations, the shape of interaction potential, spatial correlations and motion on non-equilibrium phase diagrams and the occurrence of bistability are examined. An ensemble averaged mean field model is introduced as an exact solution for completely uncorrelated ensembles. It is shown that the van der Waals interaction does not allow the occurrence of bistability, for which a finite dipolar core is required. The short-range interaction potential shape is found to have a profound influence on non-equilibrium phase diagrams, controlling the size of fluctuations in the dynamics. For a frozen system, several methods for identifying and quantifying bistable phases are introduced, and phase diagrams are reconstructed. It is shown that the temperature of external degrees of freedom, i.e. spin motion, can drive a non-equilibrium transition into the bistable phase.
Motivated by the spin self-rephasing recently observed in an atomic clock, we introduce a simple dynamical model to study the competition between dephasing and synchronization. Two spins S are taken to be initially parallel and in the plane perpendicular to an inhomogeneous magnetic field Δ that tends to dephase them. In addition, the spins are coupled by exchange interaction J that tries to keep them locked. The analytical solution of the classical dynamics shows that, there is a phase transition to a synchronized regime for sufficiently large exchange interaction J>Δ compared to the inhomogeneity. The quantum dynamics is solved analytically in four limits -- large/small J/Δ and large/small S -- and numerically in between. In sharp contrast to the classical case, the quantum solution features very rich S-dependent multiscale dynamics. For any finite S, there is no synchronization but a crossover around J=Δ between two regimes. The synchronization transition is only recovered when S→∞, approaching the classical solution in a non-trivial way. Quantum effects therefore suppress the synchronization transition.