Photon Fock States Research Articles

Optimized higher-order photon state classification by machine learning

The classification of higher-order photon emission becomes important with more methods being developed for deterministic multiphoton generation. The widely used second-order correlation g(2) is not sufficient to determine the quantum purity of higher photon Fock states. Traditional characterization methods require a large amount of photon detection events, which leads to increased measurement and computation time. Here, we demonstrate a machine learning model based on a 2D Convolutional Neural Network (CNN) for rapid classification of multiphoton Fock states up to |3⟩ with an overall accuracy of 94%. By fitting the g(3) correlation with simulated photon detection events, the model exhibits an efficient performance particularly with sparse correlation data, with 800 co-detection events to achieve an accuracy of 90%. Using the proposed experimental setup, this CNN classifier opens up the possibility for quasi-real-time classification of higher photon states, which holds broad applications in quantum technologies.

Certification of photon Fock states using second-order nonlinearity

Certifying whether a photon Fock state is present or not while preserving its quantum state is an important task that proves useful in quantum technologies. The existing methods to perform such task apply to single photons only and consume costly quantum resources. In this paper, we propose a resource-efficient scheme for certification of an arbitrary (nonvacuum) photon Fock state by using second-order nonlinearity. In particular, we utilize the correlations in both photon number and polarization of a stimulated parametric downconversion process to herald the presence and the quantum state of an incoming Fock state. The proposed scheme works excellently with a near perfect certification fidelity even when using nonideal photodetectors. We then compare our scheme with the existing ones taking into account relevant figures of merit for each method. We also present applications of our scheme in overcoming transmission loss of photons in quantum channels as well as in preparation of NOON states, $(|N\ensuremath{\rangle}|0\ensuremath{\rangle}+|0\ensuremath{\rangle}|N\ensuremath{\rangle})/\sqrt{2}$. Our paper introduces to the optical toolbox a practical technique that is beneficial for quantum communication and quantum metrology.

Quasi-diabatic propagation scheme for simulating polariton chemistry.

We generalize the quasi-diabatic (QD) propagation scheme to simulate the non-adiabatic polariton dynamics in molecule-cavity hybrid systems. The adiabatic-Fock states, which are the tensor product states of the adiabatic electronic states of the molecule and photon Fock states, are used as the locally well-defined diabatic states for the dynamics propagation. These locally well-defined diabatic states allow using any diabatic quantum dynamics methods for dynamics propagation, and the definition of these states will be updated at every nuclear time step. We use several recently developed non-adiabatic mapping approaches as the diabatic dynamics methods to simulate polariton quantum dynamics in a Shin-Metiu model coupled to an optical cavity. The results obtained from the mapping approaches provide very accurate population dynamics compared to the numerically exact method and outperform the widely used mixed quantum-classical approaches, such as the Ehrenfest dynamics and the fewest switches surface hopping approach. We envision that the generalized QD scheme developed in this work will provide a powerful tool to perform the non-adiabatic polariton simulations by allowing a direct interface between the diabatic dynamics methods and ab initio polariton information.

Quantum-state creation in nonlinear-waveguide arrays

Many photonic quantum information tasks employ single photons and linear transformations to create and manipulate quantum states of light to process information. Integrated optical systems have become useful platforms to perform these tasks. New technologies introduce new possible processes available for multimode quantum operations. Here we explore one such setup, motivated by current experiments, which is a nonlinear-waveguide array system operating in a regime of nondegenerate-frequency down-converted photons. This allows one photon to act as a herald for the other photon, which is created in a superposition of the individual waveguide channels. We demonstrate this setup's ability to generate highly nonclassical states, such as $N$-photon Fock states and NOON states.

Deterministic preparation of nonclassical states of light in cavity optomechanics

Cavity-optomechanics is an ideal platform for the generation non-Gaussian quantum states due to the anharmonic interaction between the light field and the mechanical oscillator; but exactly this interaction also impedes the preparation in pure states of the light field. In this paper we derive a driving protocol that helps to exploit the anharmonic interaction for state preparation, and that ensures that the state of the light field remains close-to-pure. This shall enable the deterministic preparation of photon Fock states or coherent superpositions thereof.

Triggered emission of indistinguishable photons from an organic dye molecule

Single molecules in solid state matrices have been proposed as sources of single photon Fock states back 20 years ago. Their success in quantum optics and in many other research fields stems from the simple recipes used in the preparation of samples, with hundreds of nominally identical and isolated molecules. Main challenges as of today for their application in photonic quantum technologies are the optimization of light extraction and the on-demand emission of indistinguishable photons. We here present Hong–Ou–Mandel (HOM) experiments with photons emitted by a single molecule of dibenzoterrylene in an anthracene nanocrystal at 3 K, under continuous wave and also pulsed excitation. A detailed theoretical model is applied, which relies on independent measurements for most experimental parameters, hence allowing for an analysis of the different contributions to the two-photon interference visibility, from residual dephasing to spectral filtering. A HOM interference visibility of more than 75% is reported, which, according to the model, is limited by the residual dephasing present at the operating temperature.

Speeding up generation of photon Fock state in a superconducting circuit via counterdiabatic driving* *Project supported by the Key Research Project in Universities of Henan Province, China (Grant Nos. 19A140016 and 20B140016), the Natural Science Foundation of Henan Province, China (Grant Nos. 212300410388 and 212300410238), and the “316” Project Plan of Xuchang University.

Optimal creation of photon Fock states is of importance for quantum information processing and state engineering. Here an efficient strategy is presented for speeding up generation of photon Fock state in a superconducting circuit via counterdiabatic driving. A transmon qubit is dispersively coupled to a quantized electrical field. We address a Λ-configuration interaction between the composite system and classical drivings. Based on two Gaussian-shaped drivings, a single-photon Fock state can be generated adiabatically. Instead of adding an auxiliary counterdiabatic driving, our concern is to modify these two Rabi drivings in the framework of shortcut to adiabaticity. Thus an accelerated operation with high efficiency can be realized in a much shorter time. Compared with the adiabatic counterpart, the shortcut-based operation is significantly insusceptible to decoherence effects. The scheme could offer a promising way to deterministically prepare photon Fock states with superconducting quantum circuits.

Multiphoton resonance and chiral transport in the generalized Rabi model

The generalized Rabi model (gRM) with both one- and two-photon coupling terms has been successfully implemented in circuit quantum electrodynamics systems. In this paper, we examine theoretically multiphoton resonances in the gRM and derive their effective Hamiltonians. With different detunings in the system, we show that all three- to six-photon resonances can be achieved by involving two intermediate states. Furthermore, we study the interplay between multiphoton resonance and chiral transport of photon Fock states in a resonator junction with broken time-reversal symmetry. Depending on the qubit-photon interaction and photon-hopping amplitude, we find that the system can demonstrate different short-time dynamics.

Fast generation of microwave photon Fock states in a superconducting nanocircuit

Abstract Optimal generation of photon Fock states is of significance for quantum information processing and state engineering. Here an efficient scheme is proposed for fast generation of photon Fock states in a superconducting nanocircuit via counterdiabatic driving. A Cooper-pair box circuit, behaving as an effective three-level artificial atom, is driven by a quantized cavity mode and two classical fields. By the technique of shortcuts to adiabaticity with counterdiabatic driving, we first generate a single-photon Fock state by performing population transfer within a composite system, consisting of the atom qutrit and microwave photons. Assisted by an auxiliary driving to initialize atom state, rapid generation of multi-photon Fock states can be addressed sequentially. Compared with an adiabatic counterpart, the shortcut-based operation in a shorter time contributes to enhance fidelity. The strategy could offer a promising avenue towards optimized creation of microwave photon Fock states with superconducting quantum circuits.

Generating microwave photon Fock states in a circuit QED via invariant-based shortcuts to adiabaticity

Optimal generation of photon Fock states is of significance to quantum science and technology. Here we develop a theoretical scheme for fast generating microwave photon Fock states in a circuit quantum electrodynamics (QED) via invariant-based shortcuts to adiabaticity. A superconducting transmon qubit is dispersively coupled to a cavity field of transmission line resonator. Two classical drivings are applied to a composite system, consisting of a transmon qubit and cavity field. In the two-photon resonance with a large intermediate-level detuning, a single-photon Fock state can be fast created by inversely engineering Rabi couplings. With the assistance of auxiliary driving, qubit state can be initialized for inducing multi-photon Fock states in the shortcut manner. Due to negligible leakage effects and high robustness, our scheme offers a potential way to rapidly prepare photon Fock states with a superconducting qubit in circuit QED.

Efficient production of large-size optical Schr\xf6dinger cat states

We present novel theory of effective realization of large-size optical Schrödinger cat states, which play an important role for quantum communication and quantum computation in the optical domain using laser sources. The treatment is based on the α-representation in infinite Hilbert space which is the decomposition of an arbitrary quantum state in terms of displaced number states characterized by the displacement amplitude α. We find analytical form of the α-representation for both even and odd Schrödinger cat states which is essential for their generation schemes. Two schemes are proposed for generating even/odd Schrödinger cat states of large size |β| (|β| ≥ 2) with high fidelity F (F ≈ 0.99). One scheme relies on an initially offline prepared two-mode entangled state with a fixed total photon number, while the other scheme uses separable photon Fock states as the input. In both schemes, generation of the desired states is heralded by the corresponding measurement outcomes. Conditions for obtaining states useful for quantum information processing are established and success probabilities for their generation are evaluated.

Adiabatic Fock-state-generation scheme using Kerr nonlinearity

We propose a theoretical scheme to deterministically generate Fock states in a Kerr cavity thorough adiabatic variation of the driving field strength and the cavity detuning. We show that the required time to generate a $n$-photon Fock state scales as the square root of $n$. Requirements for the Kerr coefficient relative to the system decoherence rate are provided as a function of desired state fidelity, indicating that the scheme is potentially realizable with the present state of the art in microwave superconducting circuits.

Unidimensional time-domain quantum optics

Choosing the right first quantization basis in quantum optics is critical for the interpretation of experimental results. The usual frequency basis is, for instance, inappropriate for short, subcycle waveforms. Deriving first quantization in time domain shows that the electromagnetic field is not directly proportional, nor even causally related, to the photonic field (the amplitude probability of a photon detection). We derive the relation between the two and calculate the statistics of the electromagnetic field for specific states in time domain, such as the single photon Fock state. We introduce the dual of the Hamiltonian in time domain and extend the concept of quadratures to all first quantization bases.

Experimental Gaussian Boson sampling

Gaussian Boson sampling (GBS) provides a highly efficient approach to make use of squeezed states from parametric down-conversion to solve a classically hard-to-solve sampling problem. The GBS protocol not only significantly enhances the photon generation probability, compared to standard Boson sampling with single photon Fock states, but also links to potential applications such as dense subgraph problems and molecular vibronic spectra. Here, we report the first experimental demonstration of GBS using squeezed-state sources with simultaneously high photon indistinguishability and collection efficiency. We implement and validate 3-, 4- and 5-photon GBS with high sampling rates of 832, 163 and 23 kHz, respectively, which is more than 4.4, 12.0, and 29.5 times faster than the previous experiments. Further, we observe a quantum speed-up on a NP-hard optimization problem when comparing with simulated thermal sampler and uniform sampler.

Fast and Unconditional All-Microwave Reset of a Superconducting Qubit.

Active qubit reset is a key operation in many quantum algorithms, and particularly in quantum error correction. Here, we experimentally demonstrate a reset scheme for a three-level transmon artificial atom coupled to a large bandwidth resonator. The reset protocol uses a microwave-induced interaction between the |f,0⟩ and |g,1⟩ states of the coupled transmon-resonator system, with |g⟩ and |f⟩ denoting the ground and second excited states of the transmon, and |0⟩ and |1⟩ the photon Fock states of the resonator. We characterize the reset process and demonstrate reinitialization of the transmon-resonator system to its ground state in less than 500ns and with 0.2% residual excitation. Our protocol is of practical interest as it has no additional architectural requirements beyond those needed for fast and efficient single-shot readout of transmons, and does not require feedback.

Higher-order nonclassicalities of finite dimensional coherent states: A comparative study

Conventional coherent states (CSs) are defined in various ways. For example, CS is defined as an infinite Poissonian expansion in Fock states, as displaced vacuum state, or as an eigenket of annihilation operator. In the infinite dimensional Hilbert space, these definitions are equivalent. However, these definitions are not equivalent for the finite dimensional systems. In this work, we present a comparative description of the lower- and higher-order nonclassical properties of the finite dimensional CSs which are also referred to as qudit CSs (QCSs). For the comparison, nonclassical properties of two types of QCSs are used: (i) nonlinear QCS produced by applying a truncated displacement operator on the vacuum and (ii) linear QCS produced by the Poissonian expansion in Fock states of the CS truncated at (d−1)-photon Fock state. The comparison is performed using a set of nonclassicality witnesses (e.g., higher order antibunching, higher order sub-Poissonian statistics, higher order squeezing, Agarwal–Tara parameter, Klyshko's criterion) and a set of quantitative measures of nonclassicality (e.g., negativity potential, concurrence potential and anticlassicality). The higher order nonclassicality witnesses have found to reveal the existence of higher order nonclassical properties of QCS for the first time.

Multiplying and detecting propagating microwave photons using inelastic Cooper-pair tunneling

The interaction between propagating microwave fields and Cooper-pair tunneling across a DC voltage-biased Josephson junction can be highly nonlinear. We show theoretically that this nonlinearity can be used to convert an incoming single microwave photon into an outgoing $n$-photon Fock state in a different mode. In this process, the electrostatic energy released in a Cooper-pair tunneling event is transferred to the outgoing Fock state, providing energy gain. The created multi-photon Fock state is frequency entangled and highly bunched. The conversion can be made reflectionless (impedance-matched) so that all incoming photons are converted to $n$-photon states. With realistic parameters multiplication ratios $n > 2$ can be reached. By two consecutive multiplications, the outgoing Fock-state number can get sufficiently large to accurately discriminate it from vacuum with linear post-amplification and power measurement. Therefore, this amplification scheme can be used as single-photon detector without dead time.

Concept of quantum timing jitter and non-Markovian limits in single-photon detection

Single atoms form a model system for understanding the limits of single photon detection. Here, we develop a non-Markov theory of single-photon absorption by a two-level atom to place limits on the absorption (transduction) time. We show the existence of a finite rise time in the probability of excitation of the atom during the absorption event which is infinitely fast in previous Markov theories. This rise time is governed by the bandwidth of the atom-field interaction spectrum and leads to a fundamental jitter in time-stamping the absorption event. Our theoretical framework captures both the weak and strong atom-field coupling regimes and sheds light on the spectral matching between the interaction bandwidth and single photon Fock state pulse spectrum. Our work opens questions whether such jitter in the absorption event can be observed in a multi-mode realistic single photon detector. Finally, we also shed light on the fundamental differences between linear and nonlinear detector outputs for single photon Fock state vs. coherent state pulses.

Cooperative polariton dynamics in feedback-coupled cavities

The emerging field of cavity spintronics utilizes the cavity magnon polariton (CMP) induced by magnon Rabi oscillations. In contrast to a single-spin quantum system, such a cooperative spin dynamics in the linear regime is governed by the classical physics of harmonic oscillators. It makes the magnon Rabi frequency independent of the photon Fock state occupation, and thereby restricts the quantum application of CMP. Here we show that a feedback cavity architecture breaks the harmonic-oscillator restriction. By increasing the feedback photon number, we observe an increase in the Rabi frequency, accompanied with the evolution of CMP to a cavity magnon triplet and a cavity magnon quintuplet. We present a theory that explains these features. Our results reveal the physics of cooperative polariton dynamics in feedback-coupled cavities, and open up new avenues for exploiting the light–matter interactions.

Multiparameter estimation with single photons—linearly-optically generated quantum entanglement beats the shotnoise limit

It was suggested in (Motes et al 2015 Phys. Rev. Lett. 114 170802) that optical networks with relatively inexpensive overheads—single photon Fock states, passive optical elements, and single photon detection—can show significant improvements over classical strategies for single-parameter estimation, when the number of modes in the network is small (). A similar case was made in (Humphreys et al 2013 Phys. Rev. Lett. 111 070403) for multi-parameter estimation, where measurement is instead made using photon-number resolving detectors. In this paper, we analytically compute the quantum Cramér–Rao bound to show these networks can have a constant-factor quantum advantage in multi-parameter estimation for even large number of modes. Additionally, we provide a simplified measurement scheme using only single-photon (on–off) detectors that is capable of approximately obtaining this sensitivity for a small number of modes.