arXiv subjects

Jorma Louko

Publications and source records attributed to Jorma Louko.

At least 19 recordsLinked to original sources

arXiv2026

When one sign is not enough: 2+1 circular motion Unruh effect at low energies

We address the circular motion Unruh effect in 2+1 spacetime dimensions, as probed by a pointlike Unruh-DeWitt detector coupled to a massless scalar field. The effective temperature due to circular acceleration, operationally defined in terms of the detector's excitation and de-excitation probabilities, is known to be much smaller than the linear acceleration Unruh temperature when the detector's energy gap is small and the interaction lasts for a long time. It was shown by Parry et al. [Class. Quant. Grav. 42, 245012 (2025), arXiv:2508.19987] that a temperature of the order of the linear acceleration Unruh temperature can nevertheless be recovered in a simultaneous long-time-small-gap double limit, using suitable classes of detector-field couplings described by asymptotically scaled switching families (ASSFs). The successful constructions presented there required the coupling to change sign. Here we prove, within the ASSF framework and under certain technical boundedness and localisation conditions, that sign changes in the detector-field coupling are in fact *necessary* for obtaining a nonvanishing limiting effective temperature. Our analysis is motivated by current work towards an experimental verification of the circular motion Unruh effect in analogue spacetime experiments.

gr-qc↗

arXiv2026

Reply to 'Comment on "Ideal clocks -- a convenient fiction"'

For a quantum scalar field that is confined in a uniformly linearly accelerated cavity in Minkowski spacetime and interacts linearly with a scalar field that is not confined in the cavity, a de-excitation probability formula was obtained in Lorek et al [Class. Quant. Grav. 32, 175003 (2015) [arXiv:1503.01025]] by a first-order perturbation theory calculation. A recent Comment by Toussaint [Class. Quant. Grav. 43, 068001 (2026) [arXiv:2607.00059] questions this formula on the grounds that the calculation in Lorek et al invokes Rindler modes both in the Rindler wedge of the accelerated cavity and in the opposing, causally disconnected Rindler wedge. In the present Reply we rederive the de-excitation formula given in Lorek et al by a perturbation theory calculation that is formulated entirely within the Rindler wedge of the accelerated cavity. We also take the opportunity to comment on the role of the two sets of Rindler modes in the calculation presented in Lorek et al.

gr-qc↗

arXiv2025

Back-action from inertial and non-inertial Unruh-DeWitt detectors revisited in covariant perturbation theory

We investigate the back-action from a spatially pointlike particle detector on a quantum scalar field, as characterised by the expectation value of the field's stress-energy tensor, without conditioning on a measurement of the detector. First, assuming the field to be initially in a zero-mean Gaussian Hadamard state in a globally hyperbolic spacetime, we evaluate the field's two-point function in second-order perturbation theory by techniques of covariant curved spacetime quantum field theory, which allow a full control of the time and space localisation of the interaction, and do not rely on field mode decompositions or non-local particle countings. The detector's two-point function splits into a deterministic and a fluctuating part, and we show that this split is maintained in the back-action. We then specialise to a two-level Unruh-DeWitt detector, prepared in an energy eigenstate, for which the back-action is fully fluctuating. We compute the renormalised stress-energy tensor for a massless scalar field in $(3+1)$-dimensional Minkowski spacetime for a general detector trajectory, using the manifestly causal two-point function. We present explicit analytic and numerical results for an inertial detector and a uniformly linearly accelerated detector, switched on in the asymptotic past. The energy flux into and out of the accelerated detector accounts exactly for the energy gained and lost by the detector in its transitions due to the Unruh effect. The same holds for the outward flux associated with de-excitations of the inertial detector, which has a vanishing excitation rate and no inward flux. A novelty with the accelerated detector is two regions of negative energy density when the detector is initially prepared in its ground state, one near the Rindler horizon that bounds the causal future of the trajectory, the other in the far future of the trajectory.

gr-qc↗

arXiv2025

Expansion-sensitive coupling of a local quantum system in de Sitter cosmology

When a local quantum system couples to a quantum field in a cosmological spacetime, the time dependence of the coupling strength is conventionally taken to reflect the design of the local quantum system but not to depend on the large-scale structure of the universe. In this paper, we consider a novel coupling that incorporates additional time dependence that reflects the cosmological expansion, as motivated by structures that appear in quantum cosmology. We focus on a conformal scalar field in a de Sitter Friedmann-Lema\^{\i}tre-Robertson-Walker cosmology with flat but compact spatial sections in 3+1 dimensions, and a comoving Unruh-DeWitt detector: the novel coupling posits the detector to couple to the scaled scalar field that appears in the conformally related static spacetime. We survey the differences between the conventional and novel coupling, for detectors that couple to the full field and detectors that couple only to specific field modes, and for detectors with proper time internal dynamics and detectors with conformal time internal dynamics. We also briefly discuss noncompact spatial sections and single-mode detectors with discontinuous time dependence. We find that the novel coupling tends to enhance the de-excitation peaks in the detector's response, particularly for single-mode detectors.

gr-qc↗

arXiv2025

Waiting around for Unruh

How long does a uniformly rotating observer need to interact with a quantum field in order to register an approximately thermal response due to the circular motion Unruh effect? We address this question for a massless scalar field in 2+1 dimensions, defining the effective temperature via the ratio of excitation and de-excitation rates of an Unruh-DeWitt detector in the long interaction time limit. In this system, the effective temperature is known to be significantly smaller than the linear motion Unruh effect prediction when the detector's energy gap is small: the effective temperature tends to zero in the small gap limit, linearly in the gap. We show that a positive small gap temperature at long interaction times can be regained via a controlled long-time-small-gap double limit, provided the detector's coupling to the field is allowed to change sign. The resulting small gap temperature depends on the parameters of the circular motion but not on the details of the detector's switching. The results broaden the energy range for pursuing an experimental verification of the circular motion Unruh effect in analogue spacetime experiments. As a mathematical tool, we provide a new implementation of the long interaction time limit that controls in a precise way the asymptotics of both the switching function and its Fourier transform.

gr-qc↗

arXiv2025

Nondestructive optomechanical detection scheme for Bose-Einstein condensates

We present a two-tone heterodyne optical readout scheme to extract unequal-time density correlations along an arbitrary stationary interaction path from a pancake-shaped Bose-Einstein condensate, using a modulated laser probe. Analysing the measurement noise both from imprecision and backaction, we identify the standard quantum limit for the signal-extraction scheme, and examine how a class of two-mode squeezed initial states can be used to push beyond this limit. As an application, we show how the readout scheme can be used for an experimentally feasible realisation of acceleration-dependence of quantum-vacuum fluctuations in the system, including the analogue spacetime circular motion Unruh effect. The scheme is adaptable beyond Bose-Einstein condensates, providing nondestructive access to unequal-time correlations in quantum fluids.

cond-mat.quant-gas↗

arXiv2025

Quenched entanglement harvesting

Ultracold fermionic atoms in an optical lattice, with a sudden position-dependent change (a quench) in the effective dispersion relation, have been proposed by Rodr\'iguez-Laguna et al as an analogue spacetime test of the Unruh effect. We provide new support for this analogue by analysing the entanglement of a scalar field in a (1 + 1)-dimensional continuum spacetime with a similar quench, and the harvesting of this entanglement by a pair of Unruh-DeWitt detectors. We present numerical evidence that the concurrence and mutual information harvested by the detectors are qualitatively similar to those in Rindler spacetime, but they exhibit a small yet noticeable variation when the energy pulse created by the quench crosses the detectors. These findings provide further motivation to implement the experimental proposal of Rodr\'iguez-Laguna et al.

gr-qc↗

arXiv2024

Deep in the knotted black hole

We consider the transition rate of a freely falling Unruh-DeWitt detector, coupled linearly to a massless scalar quantum field prepared in the Hartle-Hawking-Israel state, as a probe of the interior of a black hole. Specifically, we consider the transition rate of a detector in the spinless Ba\~nados-Teitelboim-Zanelli (BTZ) black hole as it freely falls toward and across the horizon and compare it to the corresponding situation for an $\mathbb{R}\text{P}^{2}$ geon. Both the BTZ black hole and its geon counterpart are quotients of $\text{AdS}_3$ spacetime that are identical exterior to the horizon but have different interior topologies. We find outside the horizon that the rates are qualitatively similar, but with the amplitude in the geon spacetime larger than in the BTZ case. Once the detector crosses the horizon, there are notable distinctions characterized by different discontinuities in the temporal derivative of the response rate. These discontinuities can appear outside the horizon if the detector is switched on at a sufficiently early time, within the past white hole horizon. In general, the detector can act as an `early warning system' that both spots the black hole horizon and discerns its interior topology.

gr-qc↗

arXiv2024

Probing hidden topology with quantum detectors

We consider the transition rate of a static Unruh-DeWitt detector in two $(2+1)$-dimensional black hole spacetimes that are isometric to the static Ba\~nados-Teitelboim-Zanelli black hole outside the horizon but have no asymptotically locally anti-de Sitter exterior behind the horizon. The spacetimes are the $\mathbb{R}\text{P}^{2}$ geon, with spatial topology $\mathbb{R}\text{P}^{2}\setminus\{\text{point at infinity}\}$, and the Swedish geon of \AA{}minneborg \emph{et al\/}, with spatial topology $T^{2}\setminus\{\text{point at infinity}\}$. For a conformal scalar field, prepared in the Hartle-Hawking-type state that is induced from the global vacuum on the anti-de Sitter covering space, we show numerically that the detector's transition rate distinguishes the two spacetimes, particularly at late exterior times, and we trace this phenomenon to the differences in the isometries that are broken by the quotient construction from the universal covering space. Our results provide an example in which information about the interior topology of a black hole is accessible to a quantum observer outside the black hole.

gr-qc↗

arXiv2024

Connecting the circular and drifted Rindler Unruh effects

In Minkowski spacetime quantum field theory, each stationary motion is associated with an effective, energy-dependent notion of temperature, which generalises the familiar Unruh temperature of uniform linear acceleration. Motivated by current experimental interest in circular motion, we analyse the effective temperature for drifted Rindler motion, generated by a boost and a spacelike translation (drift), and the way in which drifted Rindler motion can be smoothly (and in fact real analytically) deformed to circular motion through a third type of motion known as parator. For an Unruh-DeWitt detector coupled linearly to a massless scalar field in 2+1 and 3+1 spacetime dimensions, we establish analytic results in the limits of large gap, small gap and large drift speed. For fixed proper acceleration, the drifted Rindler temperature remains bounded in the large gap limit, in contrast to the circular motion temperature, which can be arbitrarily large in this limit. Finally, in 2+1 dimensions, we trace the vanishing of the circular motion temperature in the small gap limit to the weak decay of the Wightman function, and we show that, among all types of stationary motion in all dimensions, this phenomenon is unique to 2+1 dimensions and therein to circular and parator motion.

gr-qc↗

arXiv2024

Local quantum detection of cosmological expansion: Unruh-DeWitt in spatially compact Milne

We analyse the excitations and de-excitations of an inertial Unruh-DeWitt detector in the $(1+1)$-dimensional expanding Milne cosmology with compact spatial sections, coupled to a real massless scalar field with either untwisted or twisted boundary conditions, prepared in the conformal vacuum. We find the detector's response as a function of the energy gap, the Milne spatial circumference parameter, the interaction duration, the age of the universe at the switch-on moment, the detector's peculiar velocity at the switch-on moment, and, for the untwisted field, the state of the zero mode. Asymptotic analytic results are obtained at large energy gap and at large circumference parameter, in each case recovering the Minkowski vacuum response in the leading order, and in the double limit of small circumference parameter and late cosmological time, recovering the response in a static Minkowski cylinder. Numerical results are given in the interpolating regimes. The results confirm the detector's sensitivity to both classical and quantum properties of its environment.

gr-qc↗

arXiv2024

Circular motion in (anti-)de Sitter spacetime: thermality versus finite size

Anti-de Sitter spacetime and the static patch of de Sitter spacetime are arenas for investigating thermal and finite-size effects seen by an accelerated quantum observer. We consider an Unruh-DeWitt detector in uniform circular motion coupled to a conformal scalar field in $(2+1)$-dimensional de Sitter and anti-de Sitter spacetimes in the limit of a small cosmological constant $\Lambda$. In anti-de Sitter spacetime, where $\Lambda$ mimics spatial confinement, we find that the resonance peaks in the detector's response closely match those of a detector in Minkowski space with a cylindrical boundary, but with curvature corrections, more significant when the field has an ambient temperature. In the static patch of de Sitter spacetime, in the Euclidean vacuum, we show that the leading curvature correction to the detector's response is proportional to $\Lambda$, as in zero temperature anti-de Sitter, whilst the temperature corrections decay exponentially as $\Lambda \to 0$.

gr-qc↗

arXiv2024

Making two particle detectors in flat spacetime communicate quantumly

A communication protocol with non-zero quantum capacity is found when the two communicating parts are particle detector models in (3+1)-dimensional spacetime. In particular, as detectors, we consider two harmonic oscillators interacting with a scalar field, whose evolution is generalized for whatever background spacetime and whatever spacetime smearing of the detectors. We then specialize to Minkowski spacetime and an initial Minkowski vacuum, considering a rapid interaction between the field and the two detectors, studying the case where the receiver is static and the sender is moving. The possibility to have a quantum capacity greater than zero stems from a relative acceleration between the detectors. Indeed, no reliable quantum communication is possible when the two detectors are static or moving inertially with respect to each other, but a reliable quantum communication can be achieved between a uniformly accelerated sender and an inertial receiver.

gr-qc↗

arXiv2024

More Excitement Across the Horizon

An Unruh-DeWitt (UDW) detector falling radially into a four-dimensional Schwarzschild black hole, coupled linearly to a massless scalar field that has been prepared in the Hartle-Hawking or Unruh state, has recently been shown to exhibit a local extremum in its transition probability near the black hole horizon [K.K. Ng et al., New J. Phys. 24 (2022) 103018]. We show that a similar phenomenon is present in the transition rate of a UDW detector falling radially into a spinless Ba\~nados-Teitelboim-Zanelli (BTZ) black hole, with the scalar field prepared in the Hartle-Hawking state. We give extensive numerical results as a function of the detector's energy gap, the black hole's mass, and the detector's drop-off radius. Our results suggest that the effect is robust, motivating a search for a similar effect in other black hole spacetimes, and calling for an explanation of the physical origin of the effect.

gr-qc↗

arXiv2023

Ambient temperature versus ambient acceleration in the circular motion Unruh effect

It is well known that the experience of a linearly accelerated observer with acceleration $a$, interacting with a massless scalar field in its vacuum state in $3+1$ Minkowski spacetime, is identical to that of a static observer interacting with a massless scalar field in a thermal state of temperature $a/2\pi$ in $3+1$ Minkowski spacetime. We study the robustness of this duality by comparing an observer undergoing circular motion in a thermal bath with an observer that undergoes circular motion around a linearly accelerated trajectory. We find that in most regimes, observers in these two cases experience the field in different ways, and are generally able to tell the difference between the two cases by measuring observables localized along their trajectories.

gr-qc↗

arXiv2023

Circular motion analogue Unruh effect in a $2+1$ thermal bath: Robbing from the rich and giving to the poor

The Unruh effect states that a uniformly linearly accelerated observer with proper acceleration $a$ experiences the Minkowski vacuum as a thermal state at temperature $T_U=a/(2π)$. An observer in uniform circular motion experiences a similar effective temperature, operationally defined in terms of excitation and de-excitation rates, and physically interpretable in terms of synchrotron radiation, but this effective temperature depends not just on the acceleration but also on the orbital speed and the excitation energy. In this paper we consider an observer in uniform circular motion when the Minkowski vacuum is replaced by an ambient thermal bath, and we address the interplay of ambient temperature, Doppler effect, acceleration, and excitation energy. Specifically, we consider a massless scalar field in $2 + 1$ spacetime dimensions, probed by an Unruh-DeWitt detector, in a Minkowski (rather than proper) time formulation: this setting describes proposed analogue spacetime systems in which the effect may become experimentally testable, and in which an ambient temperature will necessarily be present. We establish analytic results for the observer's effective temperature in several asymptotic regions of the parameter space and provide numerical results in the interpolating regions, finding that an acceleration effect can be identified even when the Doppler effect dominates the overall magnitude of the response. We also identify parameter regimes where the observer sees a temperature lower than the ambient temperature, experiencing a cooling Unruh effect.

gr-qc↗

arXiv2023

Vacua in locally de Sitter cosmologies, and how to distinguish them

(1+1)-dimensional locally de Sitter Friedmann-Robertson-Walker cosmologies with compact spatial sections allow cosh, sinh and exponential evolution laws, each with a freely-specifiable spatial circumference parameter, and the value of this parameter has an invariant geometric meaning for the cosh and sinh evolution laws. We identify geometrically preferred states for a quantised massive scalar field on these cosmologies, some singled out by adiabatic criteria in the distant past, with an ambiguity remaining due to a massive zero mode, and others induced from the Euclidean vacuum on standard (1+1)-dimensional de Sitter space by a quotient construction. We show that a comoving quantum observer, modelled as an Unruh-DeWitt detector, can distinguish these states from the Euclidean vacuum on standard de Sitter space. Numerical plots are given in selected parameter regimes. We also evaluate the field's stress-energy tensor expectation value for those states that are induced from the Euclidean vacuum by a quotient construction.

gr-qc↗

arXiv2023

Unruh and analogue Unruh temperatures for circular motion in 3+1 and 2+1 dimensions

The Unruh effect states that a uniformly linearly accelerated observer with proper acceleration $a$ experiences Minkowski vacuum as a thermal state in the temperature $T_{\text{lin}} = a/(2π)$, operationally measurable via the detailed balance condition between excitation and de-excitation probabilities. An observer in uniform circular motion experiences a similar Unruh-type temperature $T_{\text{circ}}$, operationally measurable via the detailed balance condition, but $T_{\text{circ}}$ depends not just on the proper acceleration but also on the orbital radius and on the excitation energy. We establish analytic results for $T_{\text{circ}}$ for a massless scalar field in $3+1$ and $2+1$ spacetime dimensions in several asymptotic regions of the parameter space, and we give numerical results in the interpolating regions. In the ultrarelativistic limit, we verify that in $3+1$ dimensions $T_{\text{circ}}$ is of the order of $T_{\text{lin}}$ uniformly in the energy, as previously found by Unruh, but in $2+1$ dimensions $T_{\text{circ}}$ is significantly lower at low energies. We translate these results to an analogue spacetime nonrelativistic field theory in which the circular acceleration effects may become experimentally testable in the near future. We establish in particular that the circular motion analogue Unruh temperature grows arbitrarily large in the near-sonic limit, encouragingly for the experimental prospects, but the growth is weaker in effective spacetime dimension $2+1$ than in $3+1$.

gr-qc↗