Single-photon States Research Articles

Estimation of Gaussian random displacement using non-Gaussian states

In continuous-variable quantum information processing, quantum error correction of Gaussian errors requires simultaneous estimation of both quadrature components of displacements on phase space. However, quadrature operators $x$ and $p$ are non-commutative conjugate observables, whose simultaneous measurement is prohibited by the uncertainty principle. Gottesman-Kitaev-Preskill (GKP) error correction deals with this problem using complex non-Gaussian states called GKP states. On the other hand, simultaneous estimation of displacement using experimentally feasible non-Gaussian states has not been well studied. In this paper, we consider a multi-parameter estimation problem of displacements assuming an isotropic Gaussian prior distribution and allowing post-selection of measurement outcomes. We derive a lower bound for the estimation error when only Gaussian operations are used, and show that even simple non-Gaussian states such as single-photon states can beat this bound. Based on Ghosh's bound, we also obtain a lower bound for the estimation error when the maximum photon number of the input state is given. Our results reveal the role of non-Gaussianity in the estimation of displacements, and pave the way toward the error correction of Gaussian errors using experimentally feasible non-Gaussian states.

Photon Conversion and Interaction in a Quasi-Phase-Matched Microresonator

The conversion and interaction between quantum signals at the single-photon level are essential for scalable quantum photonic information technology. Using a fully optimized periodically poled lithium niobate microring, we demonstrate ultraefficient sum-frequency generation on a chip. The external quantum efficiency reaches $(65\ifmmode\pm\else\textpm\fi{}3)\mathrm{%}$ with only $(104\ifmmode\pm\else\textpm\fi{}4)$-$\ensuremath{\mu}\mathrm{W}$ pump power. At peak conversion, $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$-noise photon is created during the cavity lifetime, which meets the requirement of quantum applications using single-photon pulses. Using a pump and signal in single-photon coherent states, we directly measure the conversion probability produced by a single pump photon to be ${10}^{\ensuremath{-}5}$, which is a significant improvement from the state of the art, and the photon-photon coupling strength to be 9.1 MHz. Our results mark steady progress toward quantum nonlinear optics at the ultimate single-photon limit, with potential applications in highly integrated photonics and quantum optical computing.

Quantum hashing via single-photon states with orbital angular momentum

Quantum hashing is a promising generalization of the cryptographic hashing concept on the quantum domain. In this paper, we construct a quantum hash via a sequence of single-photon states and perform a proof-of-principle experiment using orbital angular momentum (OAM) encoding. We experimentally verify the collision resistance of the quantum hash function depending on the number of qubits in use. Based on these results, we conclude that theoretical estimates are confirmed for different bases of OAM states and the proposed technique can be useful in computational and cryptographic scenarios. The possibility of multiplexing different OAM bases can make this approach even more efficient.

Control engineering of continuous-mode single-photon states: a review

Control engineering of continuous-mode single-photon states: a review

Quantum optical coherence: From linear to nonlinear interferometers

Interferometers provide a highly sensitive means to investigate and exploit the coherence properties of light in metrology applications. However, interferometers come in various forms and exploit different properties of the optical states within. In this paper, we introduce a classification scheme that characterizes any interferometer based on the number of involved nonlinear elements by studying their influence on single-photon and photon-pair states. Several examples of specific interferometers from these more general classes are discussed, and the theory describing the expected first-order and second-order coherence measurements for single-photon and single-photon-pair input states is summarized and compared. These theoretical predictions are then tested in an innovative experimental setup that is easily able to switch between implementing an interferometer consisting of only one or two nonlinear elements. The resulting singles and coincidence rates are measured in both configurations and the results are seen to fit well with the presented theory. The measured results of coherence are tied back to the presented classification scheme, revealing that our experimental design can be useful in gaining insight into the properties of the various interferometeric setups containing different degrees of nonlinearity.

Probing nonclassical light fields with energetic witnesses in waveguide quantum electrodynamics

We analyze energy exchanges between a qubit and a resonant field propagating in a waveguide. The joint dynamics is analytically solved within a repeated interaction model. The work received by the qubit is defined as the unitary component of the field-induced energy change. Using the same definition for the field, we show that both work flows compensate each other. Focusing on the charging of a qubit battery by a pulse of light, we evidence that the work provided by a coherent field is an upper bound for the qubit ergotropy, while this bound can be violated by non-classical fields, e.g. a coherent superposition of zero- and single-photon states. Our results provide operational, energy-based witnesses to probe the non-classical nature of a light field.

Autocompensating measurement-device-independent quantum cryptography in space division multiplexing optical fibers

Single photon or biphoton states propagating in optical fibers or in free space are affected by random perturbations and imperfections that disturb the information encoded in such states and accordingly quantum key distribution is prevented. We propose three different systems for autocompensating such random perturbations and imperfections when a measurement-device-independent protocol is used. These systems correspond to different optical fibers intended for space division multiplexing and supporting collinear modes, polarization modes or codirectional modes such as few-mode optical fibers and multicore optical fibers. Accordingly, we propose different Bell-states measurement devices located at Charlie system and present simulations that confirm the importance of autocompensation. Moreover, these types of optical fibers allow the use of several transmission channels, which compensates the reduction of the bit rate due to losses.

Few-Mode-Fiber Technology Fine-tunes Losses in Quantum Communication Systems

A natural choice for quantum communication is to use the relative phase between two paths of a single-photon for information encoding. This method was nevertheless quickly identified as impractical over long distances and thus a modification based on single-photon time-bins has then become widely adopted. It however, introduces a fundamental loss, which increases with the dimension and that limits its application over long distances. Here, we are able to solve this long-standing hurdle by employing a few-mode fiber space-division multiplexing platform working with orbital angular momentum modes. In our scheme, we maintain the practicability provided by the time-bin scheme, while the quantum states are transmitted through a few-mode fiber in a configuration that does not introduce post-selection losses. We experimentally demonstrate our proposal by successfully transmitting phase-encoded single-photon states for quantum cryptography over 500 m of few-mode fiber, showing the feasibility of our scheme.

Side Channels of Information Leakage in Quantum Cryptography: Nonstrictly Single-Photon States, Different Quantum Efficiencies of Detectors, and Finite Transmitted Sequences

Side Channels of Information Leakage in Quantum Cryptography: Nonstrictly Single-Photon States, Different Quantum Efficiencies of Detectors, and Finite Transmitted Sequences

Transverse and Quantum Localization of Light: A Review on Theory and Experiments

Anderson localization is an interference effect yielding a drastic reduction of diffusion—including complete hindrance—of wave packets such as sound, electromagnetic waves, and particle wave functions in the presence of strong disorder. In optics, this effect has been observed and demonstrated unquestionably only in dimensionally reduced systems. In particular, transverse localization (TL) occurs in optical fibers, which are disordered orthogonal to and translationally invariant along the propagation direction. The resonant and tube-shaped localized states act as micro-fiber-like single-mode transmission channels. Since the proposal of the first TL models in the early eighties, the fabrication technology and experimental probing techniques took giant steps forwards: TL has been observed in photo-refractive crystals, in plastic optical fibers, and also in glassy platforms, while employing direct laser writing is now possible to tailor and “design” disorder. This review covers all these aspects that are today making TL closer to applications such as quantum communication or image transport. We first discuss nonlinear optical phenomena in the TL regime, enabling steering of optical communication channels. We further report on an experiment testing the traditional, approximate way of introducing disorder into Maxwell’s equations for the description of TL. We find that it does not agree with our findings for the average localization length. We present a new theory, which does not involve an approximation and which agrees with our findings. Finally, we report on some quantum aspects, showing how a single-photon state can be localized in some of its inner degrees of freedom and how quantum phenomena can be employed to secure a quantum communication channel.

Sending or Not-Sending Twin-Field Quantum Key Distribution with Flawed and Leaky Sources.

Twin-field quantum key distribution (TF-QKD) has attracted considerable attention and developed rapidly due to its ability to surpass the fundamental rate-distance limit of QKD. However, the device imperfections may compromise its practical implementations. The goal of this paper is to make it robust against the state preparation flaws (SPFs) and side channels at the light source. We adopt the sending or not-sending (SNS) TF-QKD protocol to accommodate the SPFs and multiple optical modes in the emitted states. We analyze that the flaws of the phase modulation can be overcome by regarding the deviation of the phase as phase noise and eliminating it with the post-selection of phase. To overcome the side channels, we extend the generalized loss-tolerant (GLT) method to the four-intensity decoy-state SNS protocol. Remarkably, by decomposing of the two-mode single-photon states, the phase error rate can be estimated with only four parameters. The practical security of the SNS protocol with flawed and leaky source can be guaranteed. Our results might constitute a crucial step towards guaranteeing the practical implementation of the SNS protocol.

Self-referenced hologram of a single photon beam

Quantitative characterization of the spatial structure of single photons is essential for free-space quantum communication and quantum imaging. We introduce an interferometric technique that enables the complete characterization of a two-dimensional probability amplitude of a single photon. Importantly, in contrast to methods that use a reference photon for the phase measurement, our technique relies on a single photon interfering with itself. Our setup comprises of a heralded single-photon source with an unknown spatial phase and a modified Mach-Zehnder interferometer with a spatial filter in one of its arms. The spatial filter removes the unknown spatial phase and the filtered beam interferes with the unaltered beam passing through the other arm of the interferometer. We experimentally confirm the feasibility of our technique by reconstructing the spatial phase of heralded single photons using the lowest order interference fringes. This technique can be applied to the characterization of arbitrary pure spatial states of single photons.

Transferring quantum entangled states between multiple single-photon-state qubits and coherent-state qubits in circuit QED

We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto n coherent-state (CS) qubits, by employing 2n microwave cavities coupled to a superconducting flux qutrit. The two logic states of a SPS qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CS qubit are encoded with two coherent states of a cavity. Because of using only one superconducting qutrit as the coupler, the circuit architecture is significantly simplified. The operation time for the state transfer does not increase with the increasing of the number of qubits. When the dissipation of the system is negligible, the quantum state can be transferred in a deterministic way since no measurement is required. Furthermore, the higher-energy intermediate level of the coupler qutrit is not excited during the entire operation and thus decoherence from the qutrit is greatly suppressed. As a specific example, we numerically demonstrate that the high-fidelity transfer of a Bell state of two SPS qubits onto two CS qubits is achievable within the present-day circuit QED technology. Finally, it is worthy to note that when the dissipation is negligible, entangled states of n CS qubits can be transferred back onto n SPS qubits by performing reverse operations. This proposal is quite general and can be extended to accomplish the same task, by employing a natural or artificial atom to couple 2n microwave or optical cavities.

QED theory for small-hole diffraction: Young diffraction from two Bethe holes

Based on a recently developed quantum theory for a two-level quantum well screen with a mesoscopic hole [J. Jung and O. Keller, Phys. Rev. A 98, 053825 (2018)] a quantum electrodynamical (QED) theory for diffraction of light from mesoscopic holes is presented. A propagator formalism is used to calculate the super $\mathbf{S}$ matrix, relating the scattered field operators to the incident field operators in the Heisenberg picture. The developed QED formalism accounts for electric dipole (ED), magnetic dipole (MD), and electric quadrupole (EQ) diffraction and it opens up for the analysis of mesoscopic hole diffraction of, e.g., squeezed, entangled, and coherent quantum states of light. The theory is exemplified via a study of Young diffraction from two mesoscopic holes paying particular attention to MD and EQ scattering. The scattering of a single-photon state composed of just two plane-wave components both with wave vectors directed perpendicular to the screen is obtained. It is shown from a detailed calculation of the polarization selection rules that the relative importance of the MD and EQ scattering varies with the scattering angle. The single-photon counting signal is determined as a function of one of the two incoming frequencies, keeping the other fixed near the two-level quantum well (Bohr) resonance.

Remote preparation of a general single-photon hybrid state

We present a technique for remotely preparing an arbitrary single-photon hybrid state between two distant nodes. This remote state preparation (RSP) is accomplished with a hyper-entangled state in polarization and time-bin degrees of freedom (DoFs) using some experimentally available optical elements and devices. In our RSP, the sender performs unitary operations on her hyper-entangled photon in accordance with her knowledge of the desired state to be transmitted. By performing a single-photon projective measurement and classical communication, the target state will be reconstructed at the remote receiver’s quantum system. Furthermore, we discuss the RSP via a partially hyper-entangled state. We expect our study can pave the way towards the investigation of long-distance quantum communication scenarios.

Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state

Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria for certification of quantum non-Gaussianity based on probability of vacuum in the original quantum state and a state transmitted through a lossy channel with transmittance T. We prove that the criteria hold for arbitrary multimode states, which is important for their applicability in experiments with broadband sources and single-photon detectors. Interestingly, our approach allows to detect quantum non-Gaussianity using only one photodetector instead of complex multiplexed photon detection schemes, at the cost of increased experimental time. We also formulate a quantum non-Gaussianity criterion based on the vacuum probability and mean photon number of the state and we show that this criterion is closely related to the criteria based on pair of vacuum probabilities. We illustrate the performance of the obtained criteria on the example of realistic imperfect single-photon states modeled as a mixture of vacuum and single-photon states with background Poissonian noise.

Can single photon excitation of two spatially separated modes lead to a violation of Bell inequality via weak-field homodyne measurements?

We reconsider the all-optical weak homodyne-measurement based experimental schemes aimed at revealing Bell nonclassicality (‘nonlocality’) of a single photon. We focus on the schemes put forward by Tan et al (TWC, 1991) and Hardy (1994). In our previous work we show that the TWC experiment can be described by a local hidden variable model, hence the claimed nonclassicality is apparent. The nonclassicality proof proposed by Hardy remains impeccable. We investigate which feature of the Hardy’s approach is crucial to disclose the nonclassicality. There are consequential differences between TWC and Hardy setups: (i) the initial state of Hardy is a superposition of a single photon excitation with vacuum in one of the input modes of a 50–50 beamsplitter. In the TWC case there is no vacuum component. (ii) In the final measurements of Hardy’s proposal the local settings are specified by the presence or absence of a local oscillator field (on/off). In the TWC case the auxiliary fields are constant, only phases are varied. We show that in Hardy’s setup the violation of local realism occurs due to the varying strength of the local oscillators. Still, one does not need to operate in the fully on/off detection scheme. Thus, the nonclassicality in a Hardy-like setup cannot be attributed to the single-photon state alone. It is a consequence of its interference with the photons from auxiliary local fields. Neither can it be attributed to the joint state of the single photon excitation and the local oscillator modes, as this state is measurement setting dependent. Despite giving spurious violations of local realism, the TWC scheme can serve as an entanglement indicator, for the TWC state. Nevertheless an analogue indicator based on intensity rates rather than just intensities overperforms it.

Selective excitation of subwavelength atomic clouds

A dense cloud of atoms with randomly changing positions exhibits coherent and incoherent scattering. We show that an atomic cloud of subwavelength dimensions can be modeled as a single scatterer where both coherent and incoherent components of the scattered photons can be fully explained based on effective multipole moments. This model allows us to arrive at a relation between the coherent and incoherent components of scattering based on the conservation of energy. Furthermore, using superposition of four plane waves, we show that one can selectively excite different multipole moments and thus tailor the scattering of the atomic cloud to control the cooperative shift, resonance linewidth, and the radiation pattern. Our approach provides a new insight into the scattering phenomena in atomic ensembles and opens a pathway towards controlling scattering for applications such as generation and manipulation of single-photon states.

Topological excitations and bound photon pairs in a superconducting quantum metamaterial

Recent discoveries in topological physics hold a promise for disorder-robust quantum systems and technologies. Topological states provide the crucial ingredient of such systems featuring increased robustness to disorder and imperfections. Here, we use an array of superconducting qubits to engineer a one-dimensional topologically nontrivial quantum metamaterial. By performing microwave spectroscopy of the fabricated array, we experimentally observe the spectrum of elementary excitations. We find not only the single-photon topological states but also the bands of exotic bound photon pairs arising due to the inherent anharmonicity of qubits. Furthermore, we detect the signatures of the two-photon bound edge-localized state which hints towards interaction-induced localization in our system. Our work demonstrates an experimental implementation of the topological model with attractive photon-photon interaction in a quantum metamaterial.

Hybrid single-photon, coherent, and vacuum states interference in the six-ports Mach-Zehnder interferometer

We present a theoretical study of the interferences between hybrid single-photon state, coherent state, and vacuum state in the designed medium of a six-ports Mach-Zehnder Interferometer (6p-MZI). The hybrid three different quantum states were simultaneously injected into the input ports of the interferometer. The derivation result demonstrated that the output state showed the statistical blend states among a substituted single-photon state, coherent state, and vacuum state. Interestingly, our calculation results attested that the maximum probability of detected photons at the individual interferometer output ports were significantly dependents on the amplitude of the inputted coherent state.