Single-photon Fock State Research Articles

Quantum state transfer in a ring geometry of optical waveguides having nonuniform couplings

The quantum state transfer of a system of N coupled waveguides in a ring geometry, where the last waveguide is coupled to the first one is considered. The coupling parameters are chosen not to be equal, but to vary according to the position of the waveguides. We examine the fidelity between different waveguides in order to check if it is possible to achieve a perfect state transfer (PST). We focused our analysis on the single-photon Fock state and the two-photon N00N state. Very high values of fidelity (> 95%) were found for both cases, but the PST was only observed for the single-photon Fock state.

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-optical excitations of semiconductor nanostructures in a microcavity using a two-band model and a single-mode quantum field

We theoretically study quantum-optical properties of one- and two-dimensional semiconductor nanostructures, where the electronic band structure is described by a two-band tight-binding model. Since the focus of our work is on analyzing quantum-optical effects of systems with a continuous band structure, many-body processes like electron-electron and electron-phonon interactions are neglected. The quantum-optical interband excitations are fully incorporated and described by a Jaynes-Cummings-type model. The exciting quantum light can be a state with arbitrary photon statistics. For simplicity, the results discussed here are limited to single-photon and two-photon Fock states. Our analytical approach is based on the eigenvalue problem and can be utilized to obtain explicit expressions for the steady-state properties of the system. Numerical simulations are based on solutions of the equations of motion and allow for a more precise analysis of the dynamics and nonresonant excitations of the system. We demonstrate that during the interaction process, a collective excitation of the conduction band is formed. For nonresonant excitations, this collective dynamics results in interesting steady states, in which the resonantly addressed eigenstates are occupied. The presented model provides a framework for microscopic simulations of quantum-optically excited extended semiconductor nanostructures.

Transfer of non-classical features and quantum states of light in circularly coupled waveguide arrays

We investigate the applicability of the circular arrays of coupled single-mode optical waveguides in transferring the non-classical state of light for quantum information processing. We study the nonclassical states of light, such as a single-photon Fock state, a two-photon NOON state, a single-mode squeezed state and a two-mode squeezed state as inputs to the lattice, which are key resources for various applications in the field of quantum information science. In addition, for comparison, we also examine a coherent state. We investigate the transport of non-classical features and quantum states of light from one waveguide mode to another. For the single and two-mode squeezed states, we perform a detailed study of the evolution of the squeezing. Our work highlights the potential of the circular arrays of optical waveguides platform for the transport of non-classical features and quantum states of light. We expect our results should have applications in the physical implementation of photonic quantum technologies.

Quantum state engineering using weak measurements

State preparation via postselected weak measurement in three wave mixing process is studied. Assuming the signal input mode prepared in a vacuum state, coherent state or squeezed vacuum state, separately, while the idler input prepared in weak coherent state and passing the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of idler beam's path, the signal output channel is prepared in single-photon Fock state, single-photon-added coherent state or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties including squeezing, signal amplification, second order correlation and Wigner functions of the weak measurement based output states are also investigated. Our scheme promising to provide alternate new effective method for producing useful nonclassical states in quantum information processing.

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.

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.

Quantum key establishment via a multimode fiber.

Quantum communication aims to provide absolutely secure transmission of secret information. State-of-the-art methods encode symbols into single photons or coherent light with much less than one photon on average. For long-distance communication, typically a single-mode fiber is used and significant effort has been devoted already to increase the data carrying capacity of a single optical line. Here we propose and demonstrate a fundamentally new concept for remote key establishment. Our method allows high-dimensional alphabets using spatial degrees of freedom by transmitting information through a light-scrambling multimode fiber and exploiting the no-cloning theorem. Eavesdropper attacks can be detected without using randomly switched mutually unbiased bases. We prove the security against a common class of intercept-resend and beam-splitting attacks with single-photon Fock states and with weak coherent light. Since it is optical fiber based, our method allows to naturally extend secure communication to larger distances. We experimentally demonstrate this new type of key exchange method by encoding information into a few-photon light pulse decomposed over guided modes of an easily available multimode fiber.

Multi-qubit phase gate on multiple resonators mediated by a superconducting bus.

We propose a one-step scheme for implementing multi-qubit phase gates on microwave photons in multiple resonators mediated by a superconducting bus in circuit quantum electrodynamics (QED) system. In the scheme, multiple single-mode resonators carry quantum information with their vacuum and single-photon Fock states, and a multi-level artificial atom acts as a quantum bus which induces the indirect interaction among resonators. The method of pulse engineering is used to shape the coupling strength between resonators and the bus so as to improve the fidelity and robustness of the scheme. We also discuss the influence of finite coherence time for the bus and resonators on gate fidelity respectively. Finally, we consider the suppression of unwanted transitions and propose the method of optimized detuning compensation for offsetting unwanted transitions, showing the feasibility of the scheme within the current experiment technology.

Superradiant parametric conversion of spin waves

Atomic-ensemble spin waves carrying single-photon Fock states exhibit nonclassical many-body correlations in-between atoms. The same correlations are inherently associated with single-photon superradiance, forming the basis of a plethora of quantum light-matter interfaces. We devise a scheme allowing the preparation of spatially-structured superradiant states in the atomic two-photon cascade using spin-wave light storage. We thus show that long-lived atomic ground-state spin waves can be converted to photon pairs opening the way towards nonlinear optics of spin waves via multi-wave mixing processes.

Nonclassicality of induced coherence without induced emission

Interference of two beams produced at separate biphoton sources was first observed more than two decades ago. The phenomenon, often called "induced coherence without induced emission", has recently gained attention after its applications to imaging, spectroscopy, and measuring biphoton correlations have been discovered. The sources used in the corresponding experiments are nonlinear crystals pumped by laser light. The use of a laser pump makes the occurrence of induced (stimulated) emission unavoidable and the effect of stimulated emission can be observed in the joint detection rate of the two beams. This fact raises the question whether the stimulated emission also lays a role in inducing the coherence. Here we investigate a case in which the crystals are pumped with a single-photon Fock state. We find that coherence is induced even though the possibility of stimulated emission is now fully ruled out. Furthermore, the joint detection rate of the two beams becomes ideally zero and does no longer change with the pump power. We illustrate our results by numerical simulations and by comparisons with experimental findings. Our results rule out any classical or semi-classical explanation of the phenomenon and also imply that similar experiments can be performed with fermions, for which stimulated emission is strictly forbidden.

Effective second-order correlation function and single-photon detection

Quantum-optical research on semiconductor single-photon sources puts special emphasis on the measurement of the second-order correlation function g(2)(τ), arguing that g(2)(0) < 1/2 implies the source field represents a good single-photon light source. We analyze the gain of information from g(2)(0) with respect to single photons. Any quantum state, for which the second-order correlation function falls below 1/2, has a nonzero projection on the single-photon Fock state. The amplitude p of this projection is arbitrary, independent of g(2)(0). However, one can extract a lower bound on the single-to-multi-photon-projection ratio. A vacuum contribution in the quantum state of light artificially increases the value of g(2)(0), cloaking actual single-photon projection. Thus, we propose an effective second-order correlation function , which takes the influence of vacuum into account and also yields lower and upper bounds on p. We consider the single-photon purity as a standard figure of merit in experiments, reinterpret it within our results and provide an effective version of that physical quantity. Besides comparing different experimental and theoretical results, we also provide a possible measurement scheme for determining .

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.

Quantum Storage of Single-Photon and Two-Photon Fock States with an All-Optical Quantum Memory.

Quantum memories are a crucial element toward efficient quantum protocols. In the continuous variables domain, such memories need to provide high fidelity with an efficiency set to one. Moreover, one needs to store complex quantum states exhibiting negative Wigner functions after storage. We report the storage of single- and two-photon Fock states in an all-optical quantum memory. The Wigner functions of these states show negativity after a storage time of several hundred nanoseconds. This is, to our knowledge, the first demonstration of the storage in the optical domain of non-Gaussian states with more than one photon, captured from an external source and characterized with homodyne detection.

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.

High production rate of single-photon and two-photon Fock states for quantum state engineering.

We report the implementation of a high-rate source of single- and two-photon states. By combining the advantages of short pulses and cavities, heralding rates as high as 200 kHz have been obtained for the single photons, as well as 250 Hz for the two-photon states. In this setup, homodyne measurements are conditioned by the heralding of the quantum states thanks to the introduction of a low-loss optical delay line in the heralded states path. This enables the detection of most of the heralded events, and fidelities reaching 68.5% (91% with correction for detection efficiency) and 50.4% (85% with correction) were obtained for the single- and two-photon states, respectively. Such high rates and fidelities in the generation of elementary Fock states may open the path for the production of complex quantum states.

Resource theory of non-Gaussian operations

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is non-increasing under the set of free super-operations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (1) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition and all Gaussian-dilatable non-Gaussian channels; and (2) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian-dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.

Qudit-Basis Universal Quantum Computation Usingχ(2)Interactions

We prove that universal quantum computation can be realized-using only linear optics and χ^{(2)} (three-wave mixing) interactions-in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ^{(2)} Hamiltonians and photon-number operators generate the full u(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-Z gate can be implemented with only linear optics and χ^{(2)} interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection or subtraction, a technique enabled by χ^{(2)} interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool, in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.