Fock States Research Articles

An Almost Deterministic Cooling by Measurements

AbstractNondeterministic measurement‐based techniques are efficient in reshaping the population distribution of a quantum system but suffer from a limited success probability of holding the system in the target state. To save the experimental cost, a two‐step protocol is proposed to cool a resonator down to the ground state with a near‐unit probability by exploiting the state‐engineering mechanisms of both conditional and unconditional measurements on an ancillary qubit. In the first step, the unconditional measurements on the ancillary qubit are applied to reshape the target resonator from a thermal state to a reserved Fock state. The measurement sequence can be efficiently optimized by reinforcement learning for maximum fidelity. In the second step, the population on the reserved state can be faithfully transferred in a stepwise way to the resonator's ground state with a near‐unit fidelity by the conditional measurements on the qubit. Properly designing the projection operator and the measurement interval enables the Kraus operator to act as a lowering operator for neighboring Fock states. Through dozens of measurements in all, the initial thermal average population of the resonator can be reduced by five orders in magnitude with a success probability of over 95%.

Wave packet dynamics of entangled q-deformed states

This paper explores the wave packet dynamics of a math-type q-deformed field interacting with atoms in a Kerr-type nonlinear medium. The primary focus is on the generation and dynamics of entanglement using the q-deformed field, with the quantification of entanglement accomplished through the von Neumann entropy. Two distinct initial q-deformed states, the q-deformed Fock state, and the q-deformed coherent state, are investigated. The entanglement dynamics reveal characteristics of periodic, quasi-periodic, and chaotic behaviour. Non-deformed initial states display wave packet near revivals and fractional revivals in entanglement dynamics while introducing q-deformation eliminates these features. The q-deformation significantly influences wave packet revivals and fractional revivals, with even a slight introduction causing their disappearance. For large values of q, the entanglement dynamics exhibit a chaotic nature. In the case of a beam splitter-type interaction applied to the initial deformed Fock state, an optimal deformation parameter q is identified, leading to maximum entanglement exceeding the non-deformed scenario.

Tailoring the nonclassicality of light states via mode detuning in waveguide beam splitters

The recent advent of integrated waveguide systems with reconfigurable propagation constants and coupling coefficients has opened the door to using waveguide detuning as a resource for readily tailoring the quantum properties of light states. Here we theoretically demonstrate that waveguide mode detuning can be used for molding the nonclassical properties of two interacting quantum optical fields in integrated waveguide couplers. In particular, we explore the states that are generated by conditional measurements when one of the input ports of the waveguide coupler is excited by coherent states, squeezed vacuum states, and thermal states, while the other port is excited by a single-photon Fock state. We explore the detuning range required to attain nonclassical states. Our findings could pave the way for a robust integrated-optics protocol, providing enhanced control and engineering capabilities over multiphoton quantum states.

Quantum-circuit refrigeration of a superconducting microwave resonator well below a single quantum

We experimentally demonstrate a recently proposed single-junction quantum-circuit refrigerator (QCR) as an tunable low-temperature environment for a superconducting 4.7 GHz resonator. With the help of a transmon qubit, we measure the populations of the different resonator Fock states, thus providing reliable access to the temperature of the engineered electromagnetic environment and its effect on the resonator. We demonstrate coherent and thermal resonator states and that the on-demand dissipation provided by the QCR can drive these to a small fraction of a photon on average, even if starting above 1 K. We observe that the QCR can be operated either with a dc bias voltage or a gigahertz rf drive, or a combination of these. The bandwidth of the rf drive is not limited by the circuit itself and consequently, we show that 2.9 GHz continuous and 10 ns pulsed drives lead to identical desired refrigeration of the resonator. These observations answer to the shortcomings of previous works where the Fock states were not resolvable and the QCR exhibited slow charging dynamics. Thus, this work introduces a versatile tool to study open quantum systems, quantum thermodynamics, and to quickly reset superconducting qubits. Published by the American Physical Society 2024

Deterministic Preparation of Optical Squeezed Cat and Gottesman-Kitaev-Preskill States.

Large-amplitude squeezed cat states and high-quality Gottesman-Kitaev-Preskill (GKP) states are essential for effective quantum error correction, yet their optical preparation has been hindered by challenges such as low success probabilities, small amplitudes, and insufficient squeezing. Addressing these limitations, our research introduces scalable optical schemes for the deterministic preparation of large-amplitude squeezed cat states from photon-number states. Fock states have the benefit of producing consistent cat states across all measurement outcomes and intrinsically provides a degree of squeezing. Notably, these squeezed cat states facilitate the deterministic generation of high-quality approximate GKP states via "breeding," showing that GKP error correction in optics is technically feasible in near-term experiments. Our schemes allow fault-tolerant quantum computation through the use of GKP error correction.

Optimal quantum metrology of two-photon absorption

Two-photon absorption (TPA) is a nonlinear optical process with wide-ranging applications from spectroscopy to super-resolution imaging. Despite this, the precise measurement and characterisation of TPA parameters are challenging due to their inherently weak nature. We study the potential of single-mode quantum light to enhance TPA parameter estimation through the quantum Fisher information (QFI). Discrete variable quantum states (defined to be a finite superposition of Fock states) are optimised to maximise the QFI for given absorption, revealing a quantum advantage compared to both the coherent state (classical) benchmark and the single-mode squeezed vacuum state. For fixed average energy n¯∈2N , the Fock state is shown to be optimal for large TPA parameters, while a superposition of vacuum and a particular Fock state is optimal for small absorption for all n¯ . This differs from single-photon absorption where the Fock state is always optimal. Notably, photon counting is demonstrated to offer optimal or nearly optimal performance compared to the QFI bound for all levels of TPA parameters for the optimised quantum probes, and their quantum advantage is shown to be robust to single-photon loss. Our findings provide insight into known limiting behaviours of Gaussian probes and their different FI scalings under photon counting ( ∝n¯2 for squeezed vacuum states versus n¯3 for coherent states). The squeezed state outperforms coherent states for small TPA parameters but underperforms in the intermediate regime, becoming comparable in the large absorption limit. This can be explained through fundamental differences between behaviours of even and odd number Fock states: the former’s QFI diverges in both large and small absorption limits, while the latter diverges only in the small absorption limit, dominating at intermediate scales.

Generation of squeezed Fock states by measurement

Generation of squeezed Fock states by measurement

Chirality-assisted enhancement of tripartite entanglement in waveguide QED

We study the generation and control of genuine tripartite entanglement among quantum emitters (QEs) that are side-coupled to one-dimensional spin-momentum locked (or chiral) waveguides. By applying the machinery of Fock state master equations along with the recently proposed concurrence fill measure of tripartite entanglement [S. Xie and J. H. Eberly, Phys. Rev. Lett. 127, 040403 (2021)], we analyze how three-photon Gaussian wavepackets can distribute entanglement among two and three QEs. We show that with a five times larger waveguide decay rate in the right direction as compared to the left direction, the maximum value of tripartite entanglement can be elevated by 35%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$35\\%$$\\end{document} as compared to the symmetric scenario where both left, and right direction decay rates are equal. Additionally, chirality can maintain the tripartite entanglement for longer than the corresponding symmetric decay rate. Finally, we study the influence of detunings and spontaneous emission on the resulting entanglement. We envision quantum networking and long-distance quantum communication as two main areas of applications of this work.

Autonomous Stabilization of Fock States in an Oscillator against Multiphoton Losses.

Fock states with a well-defined number of photons in an oscillator have shown a wide range of applications in quantum information science. Nonetheless, their usefulness has been marred by single and multiphoton losses due to unavoidable environment-induced dissipation. Though several dissipation engineering methods have been developed to counteract the leading single-photon-loss error, averting multiple-photon losses remains elusive. Here, we experimentally demonstrate a dissipation engineering method that autonomously stabilizes multiphoton Fock states against losses of multiple photons using a cascaded selective photon-addition operation in a superconducting quantum circuit. Through measuring the photon-number populations and Wigner tomography of the oscillator states, we observe a prolonged preservation of nonclassical Wigner negativities for the stabilized Fock states |N⟩ with N=1, 2, 3 for a duration of about 10ms. Furthermore, the dissipation engineering method demonstrated here also facilitates the implementation of a nonunitary operation for resetting a binomially encoded logical qubit. These results highlight potential applications in error-correctable quantum information processing against multiple-photon-loss errors.

Wigner distributions of sea quarks in the light-cone quark model

We investigate the Wigner distributions of u¯ and d¯ quarks in a proton using the overlap representation within the light cone formalism. Using the light-cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we calculate the Wigner distributions for the unpolarized/longitudinally polarized sea quarks in an unpolarized/longitudinally polarized proton. The Wigner distributions can be obtained through a Fourier transform on the generalized transverse-momentum dependent parton distributions (GTMDs). We also calculate the GTMDs of u¯ and d¯ quarks in the intermediate step. Numerical results for the Wigner distributions of u¯ and d¯ quarks in transverse momentum space, impact parameter space and the mixed plane are presented. We also study the orbital angular momentum and the spin-orbit correlations of the sea quarks. Published by the American Physical Society 2024

Importance of Strange Sea to the Charge Radii and Quadrupole Moment of $J^P=\frac{1}{2}^+,\frac{3}{2}^+$ Baryons

Abstract A statistical framework in conjugation with the principle of detailed balance is employed to examine the low-energy properties, i.e. charge radii and quadrupole moment, of JP = $\frac{1}{2}^+$ octet and JP = $\frac{3}{2}^+$ decuplet baryons. The statistical model relies on the assumption that the baryons can be expanded in terms of quark–gluon Fock states. We systematically apply operator formalism along with the statistical approach to study the charge radii and quadrupole moment of baryons. Based on the probabilities of all possible Fock states in spin, flavor, and color space, the importance of sea with quarks and gluons is studied. The individual contribution of the constituent quarks and sea (scalar, vector, and tensor sea) is explored. Due to the large mass difference between strange and nonstrange content, the SU(3) breaking effect is also investigated. The extent to which strange $q\bar{q}$ pairs are considered in sea is constrained by the mass of hadrons and the free energy of gluons, in accordance with experimental evidence. We focus on the individual contribution of strange and nonstrange sea ($g, \langle u\bar{u}\rangle$, $\langle d\bar{d}\rangle$, and $\langle s\bar{s}\rangle$) accommodability in the respective hadrons for their charge radii and quadrupole moment. The present work has been compared with various theoretical approaches and some known experimental observations. The obtained results may give valuable information for upcoming experimental findings.

Stimulated Emission of Signal Photons from Dark Matter Waves.

The manipulation of quantum states of light has resulted in significant advancements in both dark matter searches and gravitational wave detectors. Current dark matter searches operating in the microwave frequency range use nearly quantum-limited amplifiers. Future high frequency searches will use photon counting techniques to evade the standard quantum limit. We present a signal enhancement technique that utilizes a superconducting qubit to prepare a superconducting microwave cavity in a nonclassical Fock state and stimulate the emission of a photon from a dark matter wave. By initializing the cavity in an |n=4⟩ Fock state, we demonstrate a quantum enhancement technique that increases the signal photon rate and hence also the dark matter scan rate each by a factor of 2.78. Using this technique, we conduct a dark photon search in a band around 5.965GHz (24.67 μeV), where the kinetic mixing angle ε≥4.35×10^{-13} is excluded at the 90% confidence level.

All about the neutron from lattice QCD

I describe how simulations of lattice QCD using the path integral formulation provide the two basic quantum mechanical properties of QCD, its ground state in which correlation functions are calculated, and Fock state wavefunctions between which matrix elements of operators are calculated. Both constructs are stochastic, so unfortunately one gets no intuitive picture or even qualitative understanding of what they look like, nevertheless they contain and display all the subtleties of the quantum field theory. Today, these simulations provide many quantities that are impacting phenomenology and experiments. I illustrate the methods and the steps in the analysis using, as examples, three observables: the isovector charges of the nucleon, the contribution of the quark’s intrinsic spin to the nucleon spin, and the pion-nucleon sigma term.

Quantum scissor from exact generalized photon number statistics

We report the close form expressions of the photon number statistics for a generalized coherent state and a generalized photon-added coherent state, which are shown to be crucial for proposing a variety of quantum scissor operations. The analytically obtained distributions are also capable of predicting the precise laser intensity windows for realizing a variety of quantum scissors. Truncating a photon added state overcomes the selection rule of obtaining the lower order Fock states. Photon addition also enables us to obtain a higher order Fock state in a lower order superposition. The importance of circular geometry is also demonstrated for engineering such quantum scissors.

Topologically Protected Synthesizing of Fock States in a Circuit Quantum Electrodynamics Architecture

The preparation of Fock states is important for quantum information storage and processing. Herein, a two‐step protocol with topological protection for multi‐photon Fock states synthesizing in a circuit quantum electrodynamics (QED) architecture is presented. Due to photon number‐dependent vacuum Rabi splitting, the dynamics of the Jaynes–Cummings ladder in the resonant regime can be equivalent to a spin‐1/2 chain while a multi‐frequency microwave pulse is applied. Based on the topologically assisted quantum state transfer (QST)technique, multi‐photon Fock states can be conditionally generated. This method significantly reduces the complexity of experimental manipulation compared with previous multi‐step methods and is more robust as a result of topological protection. Furthermore, the protocol indicates that the circuit QED architecture could potentially provide a platform to explore the exotic phase in condensed matter.

Coherent Spin-Phonon Scattering in Facilitated Rydberg Lattices.

We investigate the dynamics of a one-dimensional spin system with facilitation constraint that can be studied using Rydberg atoms in arrays of optical tweezer traps. The elementary degrees of freedom of the system are domains of Rydberg excitations that expand ballistically through the lattice. Because of mechanical forces, Rydberg excited atoms are coupled to vibrations within their traps. At zero temperature and large trap depth, it is known that virtually excited lattice vibrations only renormalize the timescale of the ballistic propagation. However, when vibrational excitations are initially present-i.e., when the external motion of the atoms is prepared in an excited Fock state, coherent state or thermal state-resonant scattering between spin domain walls and phonons takes place. This coherent and deterministic process, which is free from disorder, leads to a reduction of the power-law exponent characterizing the expansion of spin domains. Furthermore, the spin domain dynamics is sensitive to the coherence properties of the atoms' vibrational state, such as the relative phase of coherently superimposed Fock states. Even for a translationally invariant initial state the latter manifests macroscopically in a phase-sensitive asymmetric expansion.

Generating overlap between compass states and squeezed, displaced, or Fock states

Generating overlap between compass states and squeezed, displaced, or Fock states

NONCLASSICAL PROPERTIES OF TWO-MODE DISPLACED FOCK STATE

In this paper, we investigate a variety of nonclassical properties of a two-mode displaced Fock state (TMDFS). Nonclassical properties such as sum squeezing, difference squeezing, antibunching effect, and the Cauchy-Schwarz inequality will be discussed analytically for the TMDFS. The results show that by changing the Fock state parameters between modes and the displacement parameter, the TMDFS exhibits enhanced nonclassical behaviors and makes a valuable contribution to quantum optics.

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols. We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function. As an application, we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states: a mixture of vacuum and Fock states, single-photon added thermal states, and even/odd Schrödinger cat states. It is shown that such a criterion is faithful and effective for revealing non-Gaussianity. We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.

Controlling the photon number coherence of solid-state quantum light sources for quantum cryptography

Quantum communication networks rely on quantum cryptographic protocols including quantum key distribution (QKD) based on single photons. A critical element regarding the security of QKD protocols is the photon number coherence (PNC), i.e., the phase relation between the vacuum and one-photon Fock state. To obtain single photons with the desired properties for QKD protocols, optimal excitation schemes for quantum emitters need to be selected. As emitters, we consider semiconductor quantum dots, that are known to generate on-demand single photons with high purity and indistinguishability. Exploiting two-photon excitation of a quantum dot combined with a stimulation pulse, we demonstrate the generation of high-quality single photons with a controllable degree of PNC. The main tuning knob is the pulse area giving full control from minimal to maximal PNC, while without the stimulating pulse the PNC is negligible in our setup for all pulse areas. Our approach provides a viable route toward secure communication in quantum networks.