arXiv subjects

Daniel A. Steck

Publications and source records attributed to Daniel A. Steck.

15 recordsLinked to original sources

arXiv2026

All Hilbert spaces are the same: consequences for generalized coordinates and momenta

Making use of the simple fact that all separable complex Hilbert spaces of given dimension are isomorphic, we show that there are just six basic ways to define generalized coordinate operators in Quantum Mechanics. In each case a canonically conjugate generalized momentum operator can be defined, but it may not be self-adjoint. Even in those cases we show there is always either a self-adjoint extension of the operator or a Neumark extension of the Hilbert space that produces a self-adjoint momentum operator. In one of the six cases both extensions work, thus leading to seven basic pairs of coordinate and momentum operators. We also show why there are more ways of defining basic coordinate and momentum measurements. A special role is reserved for measurements that simultaneously measure both.

quant-ph↗

arXiv2025

Atoms, Worldlines, and the Scalar Approximation

The worldline path-integral method, developed thus far for scalar fields, offers promising computational efficiency in general geometries, However, it relies so far on the scalar approximation that decomposes electromagnetic waves into two independent polarizations. In this work, we investigate different theoretical frameworks of fluctuation-induced effects and analyze the limitations of the worldline path-integral method in modeling multiple-atom Casimir-Polder interactions. In particular, we ask the question: how accurate is the scalar approximation? Using the worldline approach, it appears that a simple sum of the contributions from the two polarizations agrees with the exact Casimir-Polder force for two-atom systems. However, it turns out that this agreement is fortuitous. To enable calculations beyond two atoms via worldlines, we develop general N-atom expressions for the Casimir-Polder force within the scalar approximation. For three-body systems, the scalar worldline method fails drastically, predicting significant discrepancies in both magnitude and sign due to strong polarization mixing. Furthermore, we show that the TE/TM decomposition in the worldline method differs from that of the Green-tensor formalism, and we discuss why this is. This study highlights the inadequacy of scalar worldline models that rely on the polarization-decomposition approximation in general geometries.

quant-ph↗

arXiv2024

Pathwise Differentiation of Worldline Path Integrals

The worldline method is a powerful numerical path-integral framework for computing Casimir and Casimir-Polder energies. An important challenge arises when one desires derivatives of path-integral quantities--standard finite-difference techniques, for example, yield results of poor accuracy. In this work we present methods for computing derivatives of worldline-type path integrals of scalar fields to calculate forces, energy curvatures, and torques. In Casimir-Polder-type path integrals, which require derivatives with respect to the source point of the paths, the derivatives can be computed by a simple reweighting of the path integral. However, a partial-averaging technique is necessary to render the differentiated path integral computationally efficient. We also discuss the computation of Casimir forces, curvatures, and torques between macroscopic bodies. Here a different method is used, involving summing over the derivatives of all the intersections with a body; again, a different partial-averaging method makes the path integral efficient. To demonstrate the efficiency of the techniques, we give the results of numerical implementations of these worldline methods in atomplane and plane-plane geometries. Being quite general, the methods here should apply to path integrals outside the worldline context (e.g., financial mathematics).

quant-ph↗

arXiv2022

Anatomy of an extreme event: What can we infer about the history of a heavy-tailed random walk?

Extreme events are by nature rare and difficult to predict, yet are often much more important than frequent, typical events. An interesting counterpoint to the prediction of such events is their retrodiction -- given a process in an outlier state, how did the events leading up to this endpoint unfold? In particular, was there only a single, massive event, or was the history a composite of multiple, smaller but still significant events? To investigate this problem we take heavy-tailed stochastic processes (specifically,the symmetric, $α$-stable Lévy processes) as prototypical random walks. A natural and useful characteristic scale arises from the analysis of processes conditioned to arrive in a particular final state (Lévy bridges). For final displacements longer than this scale, the scenario of a single, long jump is most likely, even though it corresponds to a rare, extreme event. On the other hand, for small final displacements, histories involving extreme events tend to be suppressed. To further illustrate the utility of this analysis, we show how it provides an intuitive framework for understanding three problems related to boundary crossings of heavy-tailed processes. These examples illustrate how intuition fails to carry over from diffusive processes, even very close to the Gaussian limit. One example yields a computationally and conceptually useful representation of Lévy bridges that illustrates how conditioning impacts the extreme-event content of a random walk. The other examples involve the conditioned boundary-crossing problem and the ordinary first-escape problem; we discuss the observability of the latter example in experiments with laser-cooled atoms.

math.PR↗

arXiv2016

Noise reduction of a Libbrecht--Hall style current driver

The Libbrecht--Hall circuit is a well-known, low-noise current driver for narrow-linewidth diode lasers. An important feature of the circuit is a current limit to protect the laser diode. As the current approaches the maximum limit, however, the noise in the laser current increases dramatically. This paper documents this behavior and explores simple circuit modifications to alleviate this issue.

physics.ins-det↗

arXiv2016

Worldline approach for numerical computation of electromagnetic Casimir energies. I. Scalar field coupled to magnetodielectric media

We present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric (TE) polarization coupled to a dielectric medium converge to the proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte-Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. While these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.

quant-ph↗

arXiv2012

High passive-stability diode-laser design for use in atomic-physics experiments

We present the design and performance characterization of an external cavity diode-laser system optimized for high stability, low passive spectral linewidth, low cost, and ease of in-house assembly. The main cavity body is machined from a single aluminum block for robustness to temperature changes and mechanical vibrations, and features a stiff and light diffraction-grating arm to suppress low-frequency mechanical resonances. The cavity is vacuum-sealed, and a custom-molded silicone external housing further isolates the system from acoustic noise and temperature fluctuations. Beam shaping, optical isolation, and fiber coupling are integrated, and the design is easily adapted to many commonly used wavelengths. Resonance data, passive-linewidth data, and passive stability characterization of the new design demonstrate that its performance exceeds published specifications for commercial precision diode-laser systems. The design is fully documented and freely available.

physics.optics↗

arXiv2010

Cooling Atoms with a Moving One-Way Barrier

We implement and demonstrate the effectiveness of a cooling scheme using a moving, all-optical, one-way barrier to cool a sample of $^{87}$Rb atoms, achieving nearly a factor of 2 reduction in temperature. The one-way barrier, composed of two focused, Gaussian laser beams, allows atoms incident on one side to transmit, while reflecting atoms incident on the other. The one-way barrier is adiabatically swept through a sample of atoms contained in a far-off-resonant, single-beam, optical dipole trap that forms a nearly harmonic trapping potential. As the barrier moves longitudinally through the potential, atoms become trapped to one side of the barrier with reduced kinetic energy. The adiabatic translation of the barrier leaves the atoms at the bottom of the trapping potential, only minimally increasing their kinetic energy.

physics.atom-ph↗

arXiv2010

Reflection of a Particle from a Quantum Measurement

We present a generalization of continuous position measurements that accounts for a spatially inhomogeneous measurement strength. This describes many real measurement scenarios, in which the rate at which information is extracted about position has itself a spatial profile, and includes measurements that detect if a particle has crossed from one region into another. We show that such measurements can be described, in their averaged behavior, as stochastically fluctuating potentials of vanishing time average. Reasonable constraints restrict the form of the measurement to have degenerate outcomes, which tend to drive the system to spatial superposition states. We present the results of quantum-trajectory simulations for measurements with a step-function profile (a "which-way" measurement) and a Gaussian profile. We find that the particle can coherently reflect from the measurement region in both cases, despite the stochastic nature of the measurement back-action. In addition, we explore the connection to the quantum Zeno effect, where we find that the reflection probability tends to unity as the measurement strength increases. Finally, we discuss two physical realizations of a spatially varying position measurement using atoms.

quant-ph↗

arXiv2009

Dynamics of Cold Atoms Crossing a One-Way Barrier

We implemented an optical one-way potential barrier that allows ultracold $^{87}$Rb atoms to transmit through when incident on one side of the barrier but reflect from the other. This asymmetric barrier is a realization of Maxwell's demon, which can be employed to produce phase-space compression and has implications for cooling atoms and molecules not amenable to standard laser-cooling techniques. The barrier comprises two focused, Gaussian laser beams that intersect the focus of a far-off-resonant, single-beam optical dipole trap that holds the atoms. The main barrier beam presents a state-dependent potential to incident atoms, while the repumping barrier beam optically pumps atoms to a trapped state. We investigated the robustness of the barrier asymmetry to changes in the barrier beam separation, the initial atomic potential energy, the intensity of the second beam, and the detuning of the first beam. We performed simulations of the atomic dynamics in the presence of the barrier, showing that the initial three dimensional momentum distribution plays a significant role, and that light-assisted collisions are likely the dominant loss mechanism. We also carefully examined the relationship to Maxwell's demon and explicitly accounted for the apparent decrease in entropy for our particular system.

physics.atom-ph↗

arXiv2008

Experimental Realization of an Optical One-Way Barrier for Neutral Atoms

We demonstrate an asymmetric optical potential barrier for ultracold 87 Rb atoms using laser light tuned near the D_2 optical transition. Such a one-way barrier, where atoms impinging on one side are transmitted but reflected from the other, is a realization of Maxwell's demon and has important implications for cooling atoms and molecules not amenable to standard laser-cooling techniques. In our experiment, atoms are confined to a far-detuned dipole trap consisting of a single focused Gaussian beam, which is divided near the focus by the barrier. The one-way barrier consists of two focused laser beams oriented almost normal to the dipole-trap axis. The first beam is tuned to have a red (blue) detuning from the F=1 -> F' (F=2 -> F') hyperfine transitions, and thus presents a barrier only for atoms in the F=2 ground state, while letting F=1 atoms pass. The second beam pumps the atoms to F=2 on the reflecting side of the barrier, thus producing the asymmetry.

physics.atom-ph↗

arXiv2006

Fractal templates in the escape dynamics of trapped ultracold atoms

We consider the dynamic escape of a small packet of ultracold atoms launched from within an optical dipole trap. Based on a theoretical analysis of the underlying nonlinear dynamics, we predict that fractal behavior can be seen in the escape data. This data would be collected by measuring the time-dependent escape rate for packets launched over a range of angles. This fractal pattern is particularly well resolved below the Bose-Einstein transition temperature--a direct result of the extreme phase space localization of the condensate. We predict that several self-similar layers of this novel fractal should be measurable and we explain how this fractal pattern can be predicted and analyzed with recently developed techniques in symbolic dynamics.

physics.atom-ph↗

arXiv2006

A Straightforward Introduction to Continuous Quantum Measurement

We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary background material for those new to measurement theory, and describe further various aspects of continuous measurements that should be helpful to those wanting to use such measurements in applications. Specifically, we use the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables, give a tutorial on stochastic calculus, treat multiple observers and inefficient detection, examine a general form of the measurement master equation, and show how the master equation leads to information gain and disturbance. To conclude, we give a detailed treatment of imaging the resonance fluorescence from a single atom as a concrete example of how a continuous position measurement arises in a physical system.

quant-ph↗

arXiv2006

Feedback cooling of atomic motion in cavity QED

We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.

quant-ph↗

arXiv2004

Quantum Feedback Control of Atomic Motion in an Optical Cavity

We study quantum feedback cooling of atomic motion in an optical cavity as a prototypical nonlinear quantum control problem. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies.

quant-ph↗