arXiv subjects

Andreas Albrecht

Publications and source records attributed to Andreas Albrecht.

At least 19 recordsLinked to original sources

arXiv2024

A Search for Classical Subsystems in Quantum Worlds

Decoherence and einselection have been effective in explaining several features of an emergent classical world from an underlying quantum theory. However, the theory assumes a particular factorization of the global Hilbert space into constituent system and environment subsystems, as well as specially constructed Hamiltonians. In this work, we take a systematic approach to discover, given a fixed Hamiltonian, (potentially) several factorizations (or tensor product structures) of a global Hilbert space that admit a quasi-classical description of subsystems in the sense that certain states (the "pointer states") are robust to entanglement. We show that every Hamiltonian admits a pointer basis in the factorization where the energy eigenvectors are separable. Furthermore, we implement an algorithm that allows us to discover a multitude of factorizations that admit pointer states and use it to explore these quasi-classical "realms" for both random and structured Hamiltonians. We also derive several analytical forms that the Hamiltonian may take in such factorizations, each with its unique set of features. Our approach has several implications: it enables us to derive the division into quasi-classical subsystems, demonstrates that decohering subsystems do not necessarily align with our classical notion of locality, and challenges ideas expressed by some authors that the propensity of a system to exhibit classical dynamics relies on minimizing the interaction between subsystems. From a quantum foundations perspective, these results lead to interesting ramifications for relative-state interpretations. From a quantum engineering perspective, these results may be useful in characterizing decoherence free subspaces and other passive error avoidance protocols.

quant-ph↗

arXiv2022

Entanglement masquerading in the CMB

The simplest single-field inflation models capture all the relevant contributions to the patterns in the Cosmic Microwave Background (CMB) observed today. A key assumption in these models is that the quantum inflationary fluctuations that source such patterns are generated by a particular quantum state -- the Bunch-Davies (BD) state. While this is a well-motivated choice from a theoretical perspective, the question arises of whether current data can rule out other, also well motivated, choices of states. In particular, as we previously demonstrated in arXiv:2104.13410 [hep-th], entanglement is naturally and inevitably dynamically generated during inflation given the presence of a "rolling" spectator scalar field -- and the resulting entangled state will yield a primordial power spectrum with potentially measurable deviations compared to the canonical BD result. For this work we developed a perturbative framework to allow a systematic exploration of constraints on (or detection of) entangled states with Planck CMB data using Monte Carlo techniques. We have found that most entangled states accessible with our framework are consistent with the data. One would have to expand the framework to allow a greater variety of entangled states in order to saturate the Planck constraints and more systematically explore any preferences the data may have among the different possibilities.

hep-th↗

arXiv2022

Einselection, Equilibrium and Cosmology

Our observed Universe has a very strong arrow of time rooted in its low entropy starting point. This low entropy start can be related to various "tuning puzzles" about the early state of the Universe. Here we explore the relationship between the arrow of time and the emergence of classical from quantum in the hopes of ultimately gaining insights into cosmological initial conditions. Our focus is on einselection, the process whereby interactions with an environment select preferred states for a quantum system. This process plays an essential role in the emergence of classical from quantum. Studies of einselection have so far been limited to cases that exhibit an arrow of time. Here we study the ability of equilibrium systems to exhibit einselection -- and investigate whether detailed balance prevents this -- motivated by the question of whether classicality requires an arrow of time. We present calculations in the adapted Caldeira-Leggett model which demonstrate that einselection can indeed take place in equilibrium systems, and show how this phenomenon is tied to histories which express an arrow of time, despite the global equilibrium. We discuss some interesting implications of our results for cosmology and cosmological initial conditions. We are intrigued and a bit surprised by the role the consistent histories formalism has ended up playing in our analysis.

hep-th↗

arXiv2022

Quintessential Cosmological Tensions

Several cosmological tensions have emerged in light of recent data, most notably in the inferences of the parameters $H_0$ and $\sigma_8$. We explore the possibility of alleviating both these tensions {\it simultaneously} by means of the Albrecht-Skordis ``quintessence'' potential. The field can reduce the size of the sound horizon $r_s^*$ while concurrently suppressing the power in matter density fluctuations before it comes to dominate the energy density budget today. Interestingly, this rich set of dynamics is governed entirely by one free parameter that is of $\mathcal{O}(10)$ in Planck units. We find that the inferred value of $H_0$ can be increased, while that of $\sigma_8$ can be decreased, both by $\approx 1\sigma$ compared to the $\Lambda$CDM case. However, ultimately the model is disfavored by Planck and BAO data alone, compared to the standard $\Lambda$CDM model, with a $\Delta \chi^2 \approx +6$. When including large scale structure and supernova data $\Delta \chi^2 \approx +1$. We note that historically much attention has been focused on preserving the three angular scales $\theta_D$, $\theta_{EQ}$, and $\theta_s^*$ to their $\Lambda$CDM values. Our work presents an example of how, while doing so indeed maintains a relatively good fit to the CMB data for an increased number of ultra-relativistic species, it is a-priori insufficient in maintaining such a fit in more general model spaces.

astro-ph.CO↗

arXiv2022

Equilibration and "Thermalization'' in the Adapted Caldeira-Leggett model

I explore the processes of equilibration exhibited by the Adapted Caldeira-Leggett (ACL) model, a small unitary "toy model" developed for numerical studies of quantum decoherence between an SHO and an environment. I demonstrate how dephasing allows equilibration to occur in a wide variety of situations. While the finite model size and other "unphysical" aspects prevent the notions of temperature and thermalization from being generally applicable, certain primitive aspects of thermalization can be realized for particular parameter values. I link the observed behaviors to intrinsic properties of the global energy eigenstates, and argue that the phenomena I observe contain elements which might be key ingredients that lead to ergodic behavior in larger more realistic systems. The motivations for this work range from curiosity about phenomena observed in earlier calculations with the ACL model, to much larger questions related to the nature of equilibrium, thermalization and the emergence of physical laws.

quant-ph↗

arXiv2021

Barren plateaus preclude learning scramblers

Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. We prove a no-go theorem for learning an unknown scrambling process with QML, showing that any variational ansatz is highly probable to have a barren plateau landscape, i.e., cost gradients that vanish exponentially in the system size. This implies that the required resources scale exponentially even when strategies to avoid such scaling (e.g., from ansatz-based barren plateaus or No-Free-Lunch theorems) are employed. Furthermore, we numerically and analytically extend our results to approximate scramblers. Hence, our work places generic limits on the learnability of unitaries when lacking prior information.

quant-ph↗

arXiv2021

Adapted Caldeira-Leggett Model

We preset a variant of the Caldeira-Leggett (CL) model of a harmonic oscillator coupled to an environment. The CL model is a standard tool for studying the physics of decoherence. Our "adapted Caldeira-Leggett" (ACL) model is built in a finite Hilbert space which makes it suitable for numerical studies. Taking a numerical approach allows us to avoid the limitations of standard approximation schemes used with the CL model. We are able to evolve the ACL model in a fully reversible unitary manner, without the built-in time asymmetry and other assumptions that come with the master equation methods typically used. We have used the ACL model to study new topics in the field of decoherence and einselection where the full unitary evolution is essential to our work. Those results (reported in companion papers) include an examination of the relationship between einselection and the arrow of time, and studies of the very earliest stages of einselection. This paper provides details about the ACL model and our numerical methods. Our numerical approach makes it straightforward to explore and plot any property of the physical system. Thus we believe the examples and illustrations we present here may provide a helpful resource for those wishing to improve their familiarity with standard decoherence results, as well as those looking to probe the underpinnings of our companion papers. We expect the ACL model will be a useful tool for exploring additional phenomena that cannot be studied using traditional approximation schemes.

quant-ph↗

arXiv2021

Copycat process in the early stages of einselection

We identify and describe unique early time behavior of a quantum system initially in a superposition, interacting with its environment. This behavior -- the copycat process -- occurs after the system begins to decohere, but before complete einselection. To illustrate this behavior analytic solutions for the system density matrix, its eigenvalues, and eigenstates a short time after system-environment interactions begin are provided. Features of the solutions and their connection to observables are discussed, including predictions for the continued evolution of the eigenstates towards einselection, time dependence of spin expectation values, and an estimate of the system's decoherence time. In particular we explore which aspects of the early stages of decoherence exhibit quadratic evolution to leading order, and which aspects exhibit more rapid linear behavior. Many features of our early time perturbative solutions are agnostic of the spectrum of the environment. We also extend our work beyond short time perturbation theory to compare with numerical work from a companion paper.

quant-ph↗

arXiv2019

Subradiant states of quantum bits coupled to a one-dimensional waveguide

The properties of coupled emitters can differ dramatically from those of their individual constituents. Canonical examples include sub- and super-radiance, wherein the decay rate of a collective excitation is reduced or enhanced due to correlated interactions with the environment. Here, we systematically study the properties of collective excitations for regularly spaced arrays of quantum emitters coupled to a one-dimensional (1D) waveguide. We find that, for low excitation numbers, the modal properties are well-characterized by spin waves with a definite wavevector. Moreover, the decay rate of the most subradiant modes obeys a universal scaling with a cubic suppression in the number of emitters. Multi-excitation subradiant eigenstates can be built from fermionic combinations of single excitation eigenstates; such "fermionization" results in multiple excitations that spatially repel one another. We put forward a method to efficiently create and measure such subradiant states, which can be realized with superconducting qubits. These measurement protocols probe both real-space correlations (using on-site dispersive readout) and temporal correlations in the emitted field (using photon correlation techniques).

quant-ph↗

arXiv2019

Non-Gaussianity from Entanglement During Inflation

We compute the bi-spectrum of CMB temperature fluctuations for a state where the metric perturbation $ζ$ is entangled with a spectator scalar field $χ$. Novel terms in the cubic $ζ$ action coupled to the scalar can be the dominant contribution to the bi-spectrum for such states and we highlight the differences between this result and the no-entanglement bi-spectrum. New shapes can be important in the bi-spectra leading to distinctive observational signatures.

hep-th↗

arXiv2019

Critical open-system dynamics in a one-dimensional optical lattice clock

There have been concerted efforts in recent years to realize the next generation of clocks using alkaline earth atoms in an optical lattice. Assuming that the atoms are independent, such a clock would benefit from a $\sqrt{N}$ enhancement in its stability, associated with the improved signal-to-noise ratio of a large atom number $N$. An interesting question, however, is what type of atomic interactions might affect the clock dynamics, and whether these interactions are deleterious or could even be beneficial. In this work, we investigate the effect of dipole-dipole interactions, in which atoms excited during the clock protocol emit and re-absorb photons. Taking a simple system consisting of a 1D atomic array, we find that dipole-dipole interactions in fact result in an open quantum system exhibiting critical dynamics, as a set of collective excitations acquires a decay rate approaching zero in the thermodynamic limit due to subradiance. A first consequence is that the decay of atomic excited population at long times exhibits a slow power-law behavior, instead of the exponential expected for non-interacting atoms. We also find that excitations among the atoms exhibit fermionic spatial correlations at long times, due to the microscopic properties of the multi-excitation subradiant states. Interestingly, these properties cannot be captured by mean-field dynamics, suggesting the strongly interacting nature of this system. We finally characterize the time-dependent frequency shift in the atomic frequency measurement, and find that it is dominated by the interaction energy of subradiant states at long times. Furthermore, we show that the decay of the clock signal displays at long times a non-exponential behavior, which might be useful to improve the uncertainty limit with which the atomic frequency can be resolved.

quant-ph↗

arXiv2018

Cosmic Inflation: The Most Powerful Microscope in the Universe

How well can we constrain the initial quantum state of metric perturbations sourced during inflation? We exhibit an interesting new class of quantum states that entangle the scalar metric perturbations ζ with other fields such as scalars as well as the tensor metric perturbations hij. These states are theoretically consistent, for inflation that lasts close to its minimum number of e-folds. They give distinguishable signatures in the power spectrum and may be able to explain some long-standing anomalies in the CMB power spectrum. We advocate using a generalized effective theory of quantum states (of which our work is an example) that, using inflation as a powerful microscope, could provide deep insights into the quantum state of matter on the smallest scales.

hep-th↗

arXiv2018

Quantum entanglement in de Sitter space with a wall, and the decoherence of bubble universes

We study the effect of a bubble wall on the entanglement entropy of a free massive scalar field between two causally disconnected open charts in de Sitter space. We assume there is a delta-functional wall between the open charts. This can be thought of as a model of pair creation of bubble universes in de Sitter space. We first derive the Euclidean vacuum mode functions of the scalar field in the presence of the wall in the coordinates that respect the open charts. We then derive the Bogoliubov transformation between the Euclidean vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that larger walls lead to less entanglement. Our result may be regarded as evidence of decoherence of bubble universes from each other. We also note an interesting relationship between our results and discussions of the black hole firewall problem.

hep-th↗

arXiv2017

Changing optical band structure with single photons

Achieving strong interactions between individual photons enables a wide variety of exciting possibilities in quantum information science and many-body physics. Cold atoms interfaced with nanophotonic structures have emerged as a platform to realize novel forms of nonlinear interactions. In particular, when atoms are coupled to a photonic crystal waveguide (PCW), long-range atomic interactions can arise that are mediated by localized atom-photon bound states. We theoretically show that in such a system, the absorption of a single photon can change the band structure for a subsequent photon. This occurs because the first photon affects the atoms in the chain in an alternating fashion, thus leading to an effective period doubling of the system and a new optical band structure for the composite atom-nanophotonic system. We demonstrate how this mechanism can be engineered to realize a single-photon switch, where the first incoming photon switches the system from being highly transmissive to highly reflective, and analyze how signatures can be observed via non-classical correlations of the outgoing photon field.

quant-ph↗

arXiv2017

Decoherence of black hole superpositions

We consider the decoherence of a black hole "Schrödinger cat"- a non-local superposition of a Schwarzschild black hole in two distinct locations - due to the Hawking radiation it inevitably emits. An environment interacting with a system acquires information about its state, e.g. about its location. The resulting decoherence is thought to be responsible for the emergence of the classical realm of our Universe out of the quantum substrate. However, this view of the emergence of the classical is sometimes dismissed as a consequence of insufficient isolation and, hence, as non-fundamental (i.e., for practical purposes only). A black hole can never be isolated from its own Hawking radiation environment that carries information about its location. The resulting decoherence rate turns out to be given by a surprisingly simple equation that, remarkably (and in contrast to known cases of decoherence), does not involve Planck's constant $\hbar$.

quant-ph↗

arXiv2017

Multipartite Entanglement and Firewalls

Black holes offer an exciting area to explore the nature of quantum gravity. The classic work on Hawking radiation indicates that black holes should decay via quantum effects, but our ideas about how this might work at a technical level are incomplete. Recently Almheiri-Marolf-Polchinski-Sully (AMPS) have noted an apparent paradox in reconciling fundamental properties of quantum mechanics with standard beliefs about black holes. One way to resolve the paradox is to postulate the existence of a "firewall" inside the black hole horizon which prevents objects from falling smoothly toward the singularity. A fundamental limitation on the behavior of quantum entanglement known as "monogamy" plays a key role in the AMPS argument. Our goal is to study and apply many-body entanglement theory to consider the entanglement among different parts of Hawking radiation and black holes. Using the multipartite entanglement measure called negativity, we identify an example which could change the AMPS accounting of quantum entanglement and perhaps eliminate the need for a firewall. Specifically, we constructed a toy model for black hole decay which has different entanglement behavior than that assumed by AMPS. We discuss the additional steps that would be needed to bring lessons from our toy model to our understanding of realistic black holes.

gr-qc↗

arXiv2017

Modifications to Cosmological Power Spectra from Scalar-Tensor Entanglement and their Observational Consequences

We consider the effects of entanglement in the initial quantum state of scalar and tensor fluctuations during inflation. We allow the gauge-invariant scalar and tensor fluctuations to be entangled in the initial state and compute modifications to the various cosmological power spectra. We compute the angular power spectra ($C_l$'s) for some specific cases of our entangled state and discuss what signals one might expect to find in CMB data. This entanglement also can break rotational invariance, allowing for the possibility that some of the large scale anomalies in the CMB power spectrum might be explained by this mechanism.

hep-th↗

arXiv2015

Transients in finite inflation

We test a model of inflation with a fast-rolling kinetic-dominated initial condition against data from Planck using Markov chain Monte Carlo parameter estimation. We test both an $m^2 ϕ^2$ potential and the $R+R^2$ gravity model and perform a full numerical calculation of both the scalar and tensor primordial power spectra. We find a slight (though not significant) improvement in fit for this model over the standard eternal slow-roll case.

astro-ph.CO↗