arXiv subjects

Murray J. Holland

Publications and source records attributed to Murray J. Holland.

At least 19 recordsLinked to original sources

arXiv2026

Non-Relativistic Quantum Electrodynamics of Atoms in a Rotating Ring Cavity

In this paper, we derive a quantum optics model in a non-inertial rotating ring cavity from first principles. We begin with the Dirac equation in curved spacetime, add minimal coupling to the electromagnetic field, and then find the Dirac Hamiltonian for the generalized Born metric. We then formally take the non-relativistic limit by way of Foldy-Wouthuysen transformations and project onto a fermionic Fock space for the atoms' electrons, protons, and neutrons. Focusing on a protium atom, we next move from a minimal coupling gauge to a multipole expansion gauge by taking a Power-Zienau-Woolley transformation under the dipole and long-wavelength approximations. Here, we find additional terms from the rotation of the system including a rotation-induced hyperfine shift of the atomic transition which could possibly be observed experimentally even for small rotation rates. Making the electric dipole, two-level, and rotating-wave approximations, we arrive at a Jaynes-Cummings-like Hamiltonian which also accounts for rotational effects, such as the rotation-induced hyperfine shift and the Sagnac shift for the cavity's counterpropagating modes.

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arXiv2026

Nonclassical Many-Body Superradiant States with Interparticle and Spin-Momentum Entanglement

We present a cross-cavity system in which steady-state superradiance is achieved using solely collective dissipative dynamics. Two cavities symmetrically couple an ensemble of four-level atoms by driving transitions between two electronic states and two motional states along perpendicular cavity axes. Both cavities operate in the bad-cavity regime: one cavity mediates collective atomic decay, while the other cavity, together with a coherent drive, mediates collective pumping via an off-resonant Raman transition. With this, we find steady-state superradiant states that possess nonclassical properties, such as super-Poissonian photon statistics. The system thus requires a beyond mean-field description, and so we develop an exact master equation simulation technique utilizing strong symmetries of the system's jump operators. Because superradiant decay is accompanied by a momentum impulse along the corresponding cavity axis, the system exhibits substantial hybrid entanglement between the atoms' spin and motional degrees of freedom at steady state. We also demonstrate that heralded measurements of the two cavity outputs prepare a state with significant particle-particle entanglement with prospects for quantum-enhanced acceleration sensing.

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arXiv2026

Efficient Polynomial-Scaled Determination of Algebraic Entanglement Entropy Between Collective Degrees of Freedom

In this work, we explore physical systems which support not only multipartite interparticle entanglement, but also intraparticle entanglement between different degrees of freedom of the constituent particles and entanglement between different degrees of freedom of different particles, i.e., algebraic entanglement. We derive a simple method for calculating the algebraic entanglement entropy between two of the particles' degrees of freedom from collective states of the whole ensemble. Our procedure makes use of underlying symmetries in these systems, in particular permutation symmetry of the particle indices, and shows a connection between the algebraic entanglement entropy in these systems and the irreducible representations of Lie groups which describe the particles' degrees of freedom. Namely, we use the direct sum over irreducible representations to diagonalize the reduced density matrices in a block-by-block manner, then utilize the multiplicity of these irreducible representations to reproduce the results from an exponentially-scaled Hilbert space in only polynomial complexity. We use this to explore a variety of systems where the constituent particles support two degrees of freedom each with two levels, such as atoms with two electronic states and two momentum states. Notably, these systems may be exactly simulated in a polynomial-scaled Hilbert space, yet they support an algebraic entanglement entropy that grows linearly with the particle number which typically requires an exponentially-scaled Hilbert space.

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arXiv2026

Dynamical aspects of steady-state subradiance: Detailed balance and its breakdown

The dynamics of dissipative many-body quantum systems sometimes admit an emergent classical description in terms of a Markov chain even though the corresponding state space contains highly entangled states. In particular, a bad-cavity laser is a paradigm system whose dynamics can be formulated as a Markov chain in a two-dimensional state space spanned by collective angular momentum states. In this article, we investigate the connection between a dissipative phase transition that occurs in the subradiant regime of this system in the large atom number limit, and the properties of the underlying Markov chain. In one of the phases, the Markov chain approaches the detailed-balance condition with increasing atom number $N$ and hence becomes effectively time-reversible. This is caused by a collective atomic emission process that effectively reduces the Markov chain to one dimension. In the other phase, we find the emergence of time-asymmetric probability currents in the two-dimensional state space that signals a breakdown of detailed balance. This is accompanied by a macroscopic internal entropy production rate in the Markov chain that scales extensively with the atom number $N$. An observable consequence of the probability currents is a self-pulsing of the cavity light output in this phase, which can be detected as an anti-correlation dip in the intensity correlation function.

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arXiv2025

Group-Theoretic Reinforcement Learning of Dynamical Decoupling Sequences

Dynamical decoupling seeks to mitigate phase decoherence in qubits by applying a carefully designed sequence of effectively instantaneous electromagnetic pulses. Although analytic solutions exist for pulse timings that are optimal under specific noise regimes, identifying the optimal timings for a realistic noise spectrum remains challenging. We propose a reinforcement learning (RL)-based method for designing pulse sequences on qubits. Our novel action set enables the RL agent to efficiently navigate this inherently non-convex optimization landscape. The action set, derived from Thompson's group $F$, is applicable to a broad class of sequential decision problems whose states can be represented as bounded sequences. We demonstrate that our RL agent can learn pulse sequences that minimize dephasing without requiring explicit knowledge of the underlying noise spectrum. This work opens the possibility for real-time learning of optimal dynamical decoupling sequences on qubits which are dephasing-limited. The model-free nature of our algorithm suggests that the agent may ultimately learn optimal pulse sequences even in the presence of unmodeled physical effects, such as pulse errors or non-Gaussian noise.

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arXiv2025

Geometric Invariants of Quantum Metrology

We establish a previously unexplored conservation law for the Quantum Fisher Information Matrix (QFIM) expressed as follows; when the QFIM is constructed from a set of observables closed under commutation, i.e., a Lie algebra, the spectrum of the QFIM is invariant under unitary dynamics generated by these same operators. Each Lie algebra therefore endows any quantum state with a fixed "budget" of metrological sensitivity -- an intrinsic resource that we show, like optical squeezing in interferometry, cannot be amplified by symmetry-preserving operations. The Uhlmann curvature tensor (UCT) naturally inherits the same symmetry group, and so quantum incompatibility is similarly fixed. As a result, a metrological analog to Liouville's theorem appears; statistical distances, volumes, and curvatures are invariant under the evolution generated by the Lie algebra. We discuss this as it relates to the quantum analogs of classical optimality criteria. This enables one to efficiently classify useful classes of quantum states at the level of Lie algebras through geometric invariants.

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arXiv2025

Fully Collective Superradiant Lasing with Vanishing Sensitivity to Cavity Length Vibrations

To date, realization of a continuous-wave active atomic clock has been elusive primarily due to parasitic heating from spontaneous emission while repumping the atoms. Here, we propose a solution to this problem by replacing the random emission with coupling to an auxiliary cavity, making repumping a fully collective process. While it is known that collective two-level models do not possess a generic lasing threshold, we show this restriction is overcome with multi-level atoms since collective pumping and decay can be performed on distinct transitions. Using relevant atomic parameters, we find this system is capable of producing an $\mathcal{O}$(100 $μ$Hz)-linewidth continuous-wave superradiant laser. Our principal result is the potential for an operating regime with cavity length vibration sensitivity below $\mathcal{O}(10^{-14} / g)$, including a locus of parameter values where it completely vanishes even at steady-state.

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arXiv2025

Noise constraints on sensitivity scaling in super-Heisenberg quantum metrology

Quantum-enhanced metrology surpasses classical metrology by improving estimation precision scaling with a resource $N$ (e.g., particle number or energy) from $1/\sqrt{N}$ to $1/N$. Through the use of nonlinear effects, Roy and Braunstein~\cite{Roy2008} derived a $1/2^N$ scaling. However, later works argued this exponential improvement is unphysical and that even modest gains, like $1/N^2$, may vanish under noise. We show that, in the presence of small errors, the nonlinear interactions enabling metrological enhancement induce emergent errors. The errors propagate through the sensing protocol and are magnified proportional to any intended non-linear enhancement. We identify a critical value of the parameter to be estimated, for a fixed error, below which the emergent errors can be avoided.

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arXiv2024

Entangled Matter-waves for Quantum Enhanced Sensing

The ability to create and harness entanglement is crucial to the fields of quantum sensing and simulation, and ultracold atom-cavity systems offer pristine platforms for this undertaking. Here, we present a method for creating and controlling entanglement between solely the motional states of atoms in a cavity without the need for electronic interactions. We show this interaction arises from a general atom-cavity model, and discuss the role of the cavity frequency shift in response to atomic motion. This cavity response leads to many different squeezing interactions between the atomic momentum states. Furthermore, we show that when the atoms form a density grating, the collective motion leads to one-axis twisting, a many-body energy gap, and metrologically useful entanglement even in the presence of noise. Noteably, an experiment has recently demonstrated this regime leads to an effective momentum-exchange interaction between atoms in a common cavity mode. This system offers a highly tunable, many-body quantum sensor and simulator.

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arXiv2024

Reductive Quantum Phase Estimation

Estimating a quantum phase is a necessary task in a wide range of fields of quantum science. To accomplish this task, two well-known methods have been developed in distinct contexts, namely, Ramsey interferometry (RI) in atomic and molecular physics and quantum phase estimation (QPE) in quantum computing. We demonstrate that these canonical examples are instances of a larger class of phase estimation protocols, which we call reductive quantum phase estimation (RQPE) circuits. Here we present an explicit algorithm that allows one to create an RQPE circuit. This circuit distinguishes an arbitrary set of phases with a fewer number of qubits and unitary applications, thereby solving a general class of quantum hypothesis testing to which RI and QPE belong. We further demonstrate a trade-off between measurement precision and phase distinguishability, which allows one to tune the circuit to be optimal for a specific application.

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arXiv2024

Robust Quantum Sensing with Multiparameter Decorrelation

The performance of a quantum sensor is fundamentally limited by noise. This noise is particularly damaging when it becomes correlated with the readout of a target signal, caused by fluctuations of the sensor's operating parameters. These uncertainties limit sensitivity in a way that can be understood with multiparameter estimation theory. We develop a new approach, adaptable to any quantum platform, for designing robust sensing protocols that leverages multiparameter estimation theory and machine learning to decorrelate a target signal from fluctuating off-target (``nuisance'') parameters. Central to our approach is the identification of information-theoretic goals that guide a machine learning agent through an otherwise intractably large space of potential sensing protocols. As an illustrative example, we apply our approach to a reconfigurable optical lattice to design an accelerometer whose sensitivity is decorrelated from lattice depth noise. We demonstrate the effect of decorrelation on outcomes and Bayesian inferencing through statistical analysis in parameter space, and discuss implications for future applications in quantum metrology and computing.

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arXiv2024

Speeding Up Squeezing with a Periodically Driven Dicke Model

We present a simple and effective method to create highly entangled spin states on a faster timescale than that of the commonly employed one-axis twisting (OAT) model. We demonstrate that by periodically driving the Dicke Hamiltonian at a resonance frequency, the system effectively becomes a two-axis countertwisting Hamiltonian which is known to quickly create Heisenberg limit scaled entangled states. For these states we show that simple quadrature measurements can saturate the ultimate precision limit for parameter estimation determined by the quantum Cramér-Rao bound. An example experimental realization of the periodically driven scheme is discussed with the potential to quickly generate momentum entanglement in a recently described experimental vertical cavity system. We analyze effects of collective dissipation in this vertical cavity system and find that our squeezing protocol can be more robust than the previous realization of OAT.

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arXiv2023

Optimal Generators for Quantum Sensing

We propose a computationally efficient method to derive the unitary evolution that a quantum state is most sensitive to. This allows one to determine the optimal use of an entangled state for quantum sensing, even in complex systems where intuition from canonical squeezing examples breaks down. In this paper we show that the maximal obtainable sensitivity using a given quantum state is determined by the largest eigenvalue of the quantum Fisher information matrix (QFIM) and, importantly, the corresponding evolution is uniquely determined by the coinciding eigenvector. Since we optimize the process of parameter encoding rather than focusing on state preparation protocols, our scheme is relevant for any quantum sensor. This procedure naturally optimizes multiparameter estimation by determining, through the eigenvectors of the QFIM, the maximal set of commuting observables with optimal sensitivity.

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arXiv2023

Cavity-Mediated Collective Momentum-Exchange Interactions

Quantum simulation and sensing hold great promise for providing new insights into nature, from understanding complex interacting systems to searching for undiscovered physics. Large ensembles of laser-cooled atoms interacting via infinite-range photon mediated interactions are a powerful platform for both endeavours. Here, we realize for the first time momentum-exchange interactions in which atoms exchange their momentum states via collective emission and absorption of photons from a common cavity mode. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer, which is useful for entanglement generation. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing, akin to Mössbauer spectroscopy. The tunable momentum-exchange interaction provides a new capability for quantum interaction-enhanced matter-wave interferometry and for realizing exotic behaviors including simulations of superconductors and dynamical gauge fields.

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arXiv2022

Beyond one-axis twisting: Simultaneous spin-momentum squeezing

The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to $SU(2)$ rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a non-linear Hamiltonian. We introduce a novel method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in $SU(4)$, thereby creating the opportunity for dynamics not possible in typical $SU(2)$ one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multi-parameter or auxiliary measurement schemes than those prepared by standard spin squeezing.

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arXiv2022

Mean-field Floquet theory for a three-level cold-atom laser

We present a theoretical description for a lasing scheme for atoms with three internal levels in a $V$-configuration and interacting with an optical cavity. The use of a $V$-level system allows for an efficient closed lasing cycle to be sustained on a dipole-forbidden transition without the need for incoherent repumping. This is made possible by utilizing an additional dipole-allowed transition. We determine the lasing threshold and emission frequency by performing a stability analysis of the non-lasing solution. In the lasing regime, we use a mean-field Floquet method (MFFM) to calculate the lasing intensity and emission frequency. This MFFM predicts the lasing transition to be accompanied by the breaking of a continuous $U(1)$ symmetry in a single Fourier component of the total field. In addition, we use the MFFM to derive bistable lasing and non-lasing solutions that highlight the non-linear nature of this system. We then test the bistability by studying hysteresis when slowly ramping external parameters across the threshold and back. Furthermore, we also compare our mean-field results to a second-order cumulant approach. The work provides simple methods for understanding complex physics that occur in cold atom lasers with narrow line transitions.

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arXiv2022

Lindblad master equations for quantum systems coupled to dissipative bosonic modes

We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke phase transition and gives the correct steady state. In addition, we compare the dynamics using exact diagonalization and numerical integration of the master equation with the predictions of semiclassical trajectories. We finally test the performance of our formalism by studying the relaxation of a NOON state and show that the dynamics captures quantum metastability beyond the mean-field approximation.

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arXiv2022

Adiabatic Control of Decoherence-Free-Subspaces in an Open Collective System

We propose a method to adiabatically control an atomic ensemble using a decoherence-free subspace (DFS) within a dissipative cavity. We can engineer a specific eigenstate of the system's Lindblad jump operators by injecting a field into the cavity which deconstructively interferes with the emission amplitude of the ensemble. In contrast to previous adiabatic DFS proposals, our scheme creates a DFS in the presence of collective decoherence. We therefore have the ability to engineer states that have high multi-particle entanglements which may be exploited for quantum information science or metrology. We further demonstrate a more optimized driving scheme that utilizes the knowledge of possible diabatic evolution gained from the so-called adiabatic criteria. This allows us to evolve to a desired state with exceptionally high fidelity on a time scale that does not depend on the number of atoms in the ensemble. By engineering the DFS eigenstate adiabatically, our method allows for faster state preparation than previous schemes that rely on damping into a desired state solely using dissipation.

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