Holographic Geometry Research Articles

Bridging two quantum quench problems — local joining quantum quench and Möbius quench — and their holographic dual descriptions

We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the Möbius quench, in the context of (1 + 1)-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined at t = 0. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, after t = 0, let it time-evolve by the so-called Möbius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the Möbius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics.

Twisted holography without conformal symmetry

We discuss the notion of translation-invariant vacua for 2d chiral algebras and relate it to the notion of the associated variety. The two-dimensional chiral algebra associated to four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 U(N) SYM has a conjectural holographic dual involving the B-model topological string theory. We study the effect of non-zero vacuum expectation values on the chiral algebra correlation functions and derive a holographic dual Calabi-Yau geometry. We test our proposal by a large N analysis of correlation functions of determinant operators, whose saddles can be matched with semi-classical configurations of “Giant Graviton” D-branes in the bulk.

Digital holographic interferometry method for tracking detector modules displacement

In high energy particle physics scattering experiments, the precision of the reconstructed particle tracks can be fundamental. For this reason, a method for detecting the displacement of tracking detector modules is developed. The modules are silicon planes mounted on a frame and used in the MUonE project, which aims at a precision measurement of the scattering angle of elastic muon-electron scattering. From the scattering angle, the hadronic contribution to the anomalous magnetic moment of the muon is extracted. To achieve the desired accuracy, the position of the tracking detector planes must be monitored. The allowable relative displacements must be less than 10 μ m. To meet the specifications and to monitor as large an area of the detector as possible, a digital holographic interferometer was developed. It is based on a novel lens-less design in off-axis holographic geometry. Light from a fiber-coupled laser source is split by a fiber beam splitter, with one output used to illuminate the detector plane and the other for the reference beam. The two beams produce an interference pattern on a CMOS image sensor. To obtain relative displacement information, successive images are superimposed on an initial reference image and reconstructed by solving the Rayleigh-Sommerfeld diffraction integral taking into account the spherical wavefronts of the beams. The interference fringes that appear in the reconstructed holographic image provide a measure of the relative displacement of the detector plane compared to the initial position. The performance of the reconstruction method used was verified with the proposed setup at a real tracking station.

Randomness assisted in-line holography with deep learning

We propose and demonstrate a holographic imaging scheme exploiting random illuminations for recording hologram and then applying numerical reconstruction and twin image removal. We use an in-line holographic geometry to record the hologram in terms of the second-order correlation and apply the numerical approach to reconstruct the recorded hologram. This strategy helps to reconstruct high-quality quantitative images in comparison to the conventional holography where the hologram is recorded in the intensity rather than the second-order intensity correlation. The twin image issue of the in-line holographic scheme is resolved by an unsupervised deep learning based method using an auto-encoder scheme. Proposed learning technique leverages the main characteristic of autoencoders to perform blind single-shot hologram reconstruction, and this does not require a dataset of samples with available ground truth for training and can reconstruct the hologram solely from the captured sample. Experimental results are presented for two objects, and a comparison of the reconstruction quality is given between the conventional inline holography and the one obtained with the proposed technique.

Entanglement and geometry from subalgebras of the Virasoro algebra

In this work we study families of generalised coherent states constructed from SL(2,R) subalgebras of the Virasoro algebra in two-dimensional conformal field theories. We derive the energy density and entanglement entropy and discuss their equivalence with analogous quantities computed in locally excited states. Moreover, we analyze their dual, holographic geometries and reproduce entanglement entropies from the Ryu-Takayanagi prescription. Finally, we outline possible applications of this universal class of states to operator growth and inhomogeneous quenches.

Holographic recordings without compromise

AbstractWidely tunable continuous‐wave optical parametric oscillator (OPO) systems help meet the demands on holographic optical elements (HOEs) for many use cases, including head‐up displays and augmented reality devices. The wide tuning range allows for direct adjustment of the replay wavelength with little to no need for modification of the holographic recording geometry. HOEs fabricated using these OPO systems in conjunction with advanced photopolymer materials offer precisely controlled replay properties and exceptional diffraction efficiency.

Dual geometry of entanglement entropy via deep learning

For a given entanglement entropy of quantum field theory, we investigate how to reconstruct its dual geometry by applying the Ryu-Takayanagi formula and the deep learning method. In the holographic setup, the radial coordinate is identified with the energy scale of the dual quantum field theory. Therefore, the holographic dual geometry can describe how physical properties of a quantum field theory change along the renormalization group flow. Intriguingly, we show that the reconstructed geometry only from the entanglement entropy data can give us more information about other physical properties like thermodynamic quantities in the infrared region.

Critical distance and Crofton form in confining geometries

For two symmetric strips with equal and finite size and in the background of several confining geometries, we numerically calculate the critical distance between these two mixed systems where the mutual information between them drops to zero and show that this quantity could be a useful correlation measure in probing the phase structures of holographic QCD models. The models that we consider here are Sakai–Sugimoto and deformed Sakai–Sugimoto, Klebanov–Tseytlin and Maldacena–Nunez. For evaluating the structures of these holographic supergravity geometries from the perspective of the bulk reconstruction, we also calculate their Crofton forms and show that there is a universal behavior in the confining backgrounds where a “well functionality” is present around the IR cut-off point, and far from the IR wall the scalar part of the Crofton form would become constant, demonstrating the effects of the wall of the confining models on the phase structures. This work is the shorter version of our previous work arXiv:2110.12970 (Ghodrati, Phys. Rev. D 104(4):046004, 2021) with few more results about the connections between phases.

Holographic path-integral optimization

In this work we elaborate on holographic description of the path-integral optimization in conformal field theories (CFT) using Hartle-Hawking wave functions in Anti-de Sitter spacetimes. We argue that the maximization of the Hartle-Hawking wave function is equivalent to the path-integral optimization procedure in CFT. In particular, we show that metrics that maximize gravity wave functions computed in particular holographic geometries, precisely match those derived in the path-integral optimization procedure for their dual CFT states. The present work is a detailed version of [1] and contains many new results such as analysis of excited states in various dimensions including JT gravity, and a new way of estimating holographic path-integral complexity from Hartle-Hawking wave functions. Finally, we generalize the analysis to Lorentzian Anti-de Sitter and de Sitter geometries and use it to shed light on path-integral optimization in Lorentzian CFTs.

Interferometric Constraints on Spacelike Coherent Rotational Fluctuations.

Precision measurements are reported of the cross-spectrum of rotationally induced differential position displacements in a pair of colocated 39m long, high-power Michelson interferometers. One arm of each interferometer is bent 90° near its midpoint to obtain sensitivity to rotations about an axis normal to the plane of the instrument. The instrument achieves quantum-limited sensing of spatially correlated signals in a broad frequency band extending beyond the 3.9-MHz inverse light travel time of the apparatus. For stationary signals with bandwidth Δf>10 kHz, the sensitivity to rotation-induced strain h of classical or exotic origin surpasses CSD_{δh}<t_{P}/2, where t_{P}=5.39×10^{-44} s is the Planck time. This measurement is used to constrain a semiclassical model of nonlocally coherent rotational degrees of freedom of spacetime, which have been conjectured to emerge in holographic quantum geometry but are not present in a classical metric.

Complexity growth of operators in the SYK model and in JT gravity

The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly important to understand how these microscopically defined measures of complexity are related to notions of complexity defined in terms of a dual holographic geometry, such as complexity-volume (CV) duality. Here we study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in Jackiw-Teitelboim (JT) gravity. We compare a microscopic definition of complexity in the SYK model known as K-complexity to calculations using CV duality in JT gravity and find that both quantities show an exponential-to-linear growth behavior. We also calculate the growth of operator size under time evolution and find connections between size and complexity. While the notion of operator size saturates at the scrambling time, our study suggests that complexity, which is well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution at both early and late times.

Geometric secret sharing in a model of Hawking radiation

We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This “inception black hole” can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER=EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed “island formula”. We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.

Holographic integral geometry with time dependence

We write down Crofton formulas — expressions that compute lengths of space- like curves in asymptotically AdS3 geometries as integrals over kinematic space — which apply when the curve and/or the background spacetime is time-dependent. Relative to their static predecessor, the time-dependent Crofton formulas display several new features, whose origin is the local null rotation symmetry of the bulk geometry. In pure AdS3 where null rotations are global symmetries, the Crofton formulas simplify and become integrals over the null planes, which intersect the bulk curve.

Simulation of digital holographic recording and reconstruction using a generalized matrix method.

In recent years, research efforts in the field of digital holography have expanded significantly, due to the ability to obtain high-resolution intensity and phase images. The information contained in these images have become of great interest to the machine learning community, with applications spanning a wide portfolio of research areas, including bioengineering. In this work, we seek to demonstrate a high-fidelity simulation of holographic recording. By accurately and numerically simulating the propagation of a coherent light source through a series of optical elements and the object itself, we accurately predict the optical interference of the object and reference wave at the recording plane, including diffraction effects, aberrations, and speckle. We show that the optical transformation that predicts the complex field at the recording plane can be generalized for arbitrary holographic recording configurations using a matrix method. In addition, we provide a detailed description of digital phase reconstruction and aberration compensation for a variety of off-axis holographic configurations. Reconstruction errors are presented for the various holographic recording geometries and complex field objects. While the primary objective of this work is not to evaluate phase reconstruction approaches, the reconstruction of simulated holograms provides validation of the generalized simulation method. The long-term goal of this work is that the generalized holographic simulation motivates the use of phase reconstruction of the simulated holograms to populate databases for training machine-learning algorithms aimed at classifying relevant objects recorded through a variety of holographic setups.

Superconformal block from holographic geometry

We explicitly construct the holographic dual configuration for the four dimensional mathcal{N} = 4 superconformal block containing half-BPS scalar primary operators by considering its full AdS5× S5 dual geometry. We extend the embedding space formalism and the related Harmonic analysis to general d-dimensional sphere Sd, and obtain precisely the R-symmetry contribution to the half-BPS scalar superconformal blocks, which we refer as “R-symmetry block”. We also observe that the R-symmetry quadratic Casimir operator can be mapped to BC2 Calogero-Sutherland system Hamiltonian, such that R-symmetry block is in terms identified as its bound state wave function.

Complexity and time

For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated with the path. This quantum time estimator is fully characterized by the Lyapunov generator of the path and the corresponding quantum Fisher information. The computational metric associated with this definition of computational complexity leads to a natural characterization of cost factors on the Lie algebra generators. Operator complexity growth in time is analyzed from this perspective leading to a simple characterization of Lyapunov exponent in case of chaotic Hamiltonians. The connection between complexity and entropy is expressed using the relation between quantum Fisher information about quantum time estimation and von Neumann entropy. This relation suggest a natural bound on computational complexity that generalizes the standard time energy quantum uncertainty. The connection between Lyapunov and modular Hamiltonian is briefly discussed. In the case of theories with holographic duals and for those reduced density matrix defined by tracing over a bounded region of the bulk, quantum estimation theory is crucial to estimate quantum mechanically the geometry of the tracing region. It is suggested that the corresponding quantum Fisher information associated with this estimation problem is at the root of the holographic bulk geometry.

Holographic geometry for nonrelativistic systems emerging from generalized flow equations

An intriguing result presented by two of the present authors is that an anti de Sitter space can be derived from a conformal field theory by considering a flow equation. A natural expectation is that given a certain data on the boundary system, the associated geometry would be able to emerge from a flow, even beyond the conformal case. As a step along this line, we examine this scenario for non-relativistic systems with anisotropic scaling symmetries, such as Lifshitz field theories and Schr\"odinger invariant theories. In consequence we obtain a new hybrid geometry of Lifshitz and Schr\"odinger spacetimes as a general holographic geometry in this framework. We confirm that this geometry reduces to each of them by considering special non-relativistic models.

Holographic quantum circuits from splitting/joining local quenches

We study three different types of local quenches (local operator, splitting and joining) in both the free fermion and holographic CFTs in two dimensions. We show that the computation of a quantity called entanglement density, provides a systematic method to capture essential properties of local quenches. This allows us to clearly understand the differences between the free and holographic CFTs as well as the distinctions between three local quenches. We also analyze holographic geometries of splitting/joining local quenches using the AdS/BCFT prescription. We show that they are essentially described by time evolutions of boundary surfaces in the bulk AdS. We find that the logarithmic time evolution of entanglement entropy arises from the region behind the Poincaré horizon as well as the evolutions of boundary surfaces. In the CFT side, our analysis of entanglement density suggests such a logarithmic growth is due to initial non-local quantum entanglement just after the quench. Finally, by combining our results, we propose a new class of gravity duals, which are analogous to quantum circuits or tensor networks such as MERA, based on the AdS/BCFT construction.

AdS vacuum bubbles, holography and dual RG flows

We explore the holographic properties of non-perturbative vacuum decay in anti-de Sitter () geometries. To this end, we consider a gravitational theory in a metastable state, which decays into an of lower vacuum energy via bubble nucleation, and we employ the Ryu–Takayanagi conjecture to compute the entanglement entropy in its alleged holographic dual. Our analysis connects the nucleation and growth of a vacuum bubble to a relevant deformation and a subsequent renormalization group (RG) flow in the boundary theory, with a c-function. We provide some evidence for the claim and comment on the holographic interpretation of off-centred or multiple bubbles. We also frame the issue in the formalism of Holographic Integral Geometry, highlighting some consequences on the structure of the holographic RG flow and recovering the standard holographic RG as a limiting case.

Demonstration of stimulated photon echo isolation using interferometric cancellation.

An alternative to phase-matched angled beam spatial-spectral holographic grating geometries for separating stimulated photon echoes (SPEs) from the probing pulse is proposed and demonstrated. By use of a Mach-Zehnder geometry with inhomogeneously broadened medium in both paths, the SPE can be interferometrically isolated from the generating probe pulse. This interferometric-based technique is well suited to waveguide geometries, which have benefits for future quantum and classical optical signal processing applications such as quantum memories, correlation, and efficient cryogenic microwave-to-optical conversion. Experimental demonstrations showing interferometric-based isolation in Tm3+-doped LiNbO3 at 3.2K are performed and analyzed.