Engineering quantum states of light represents a crucial task in the vast majority of photonic quantum technology applications. Direct manipulation of the number of photons in the light signal, such as single-photon subtraction and addition, proved to be an efficient strategy for the task. Here we propose an adaptive multi-photon subtraction scheme where a particular subtraction task is conditioned by all previous subtraction events in order to maximize the probability of successful subtraction. We theoretically illustrate this technique on the model example of conversion of Fock states via photon subtraction. We also experimentally demonstrate the core building block of the proposal by implementing a feedforward-assisted conversion of two-photon state to a single-photon state. Our experiment combines two elementary photon subtraction blocks where the splitting ratio of the second subtraction beam splitter is affected by the measurement result from the first subtraction block in real time using an ultra-fast feedforward loop. The reported optimized photon subtraction scheme applies to a broad range of photonic states, including highly nonclassical Fock states and squeezed light, advancing the photonic quantum toolbox.
Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with large photon number remains challenging. We present and analyze a bootstrapped approach for non-deterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a beamsplitter. We show that by employing state recycling we are able to exponentially improve the preparation rate over conventional schemes, allowing the efficient preparation of large Fock states. The …
We report an optical one-way quantum computing experiment with stationary quantum memory involved. First we create a hybrid four-qubit cluster state with two qubits propagating as photons and the other two stationary and stored in a laser-cooled atomic-ensemble quantum memory, and characterize it with entanglement witness and quantum state tomography. Then, by making use of this cluster state and fast operations of electro-optic modulators, we realize memory-assisted feedforward operations and demonstrate deterministic single-qubit rotation as an example.
We consider optical tomography of photon Fock state superpositions in connection with recent experimental achievements. The emphasis is put on the fact that it suffices to represent the measured tomogram as a main result of the experiment. We suggest a test for checking the correctness of experimental data. Explicit expressions for optical tomograms of Fock state superpositions are given in terms of Hermite polynomials. Particular cases of vacuum and low photon-number state superposition are considered as well as influence of thermal noise on state purity is studied.
We analyze a set of models frequently appearing in quantum optical settings by expressing their Hamiltonians in terms of Fock-state lattices. The few degrees-of-freedom of such models, together with the system symmetries, make the emerging Fock-state lattices rather simple such that they can be linked to known lattice models from the condensed matter community. This sheds new light on known quantum optical systems. While we provide a rather long list of models and their corresponding Fock-state lattices, we pick a few ones in order to demonstrate the strength of the method. The three-mode boso…
We derive the maximum success probability of the circuits with passive linear optics for expanding an N-photon W state to an (N + n)-photon W state, by accessing only one photon of the initial W state and adding n photons in a Fock state. We show that the maximum success probability is achieved by a polarization-dependent beamsplitter and n-1 polarization-independent beamsplitters.
Quantum nondemolition theory has been well understood for a number of decades, however, applications of such techniques remain limited owing to the increased complexity that these techniques require. In this paper, quantum nondemolition theory is used to investigate the performance of a real world device, an electro-optic feed-forward intensity noise eater. It is shown that by replacing the typical beamsplitter in such a device with a single pass second harmonic generation followed by a dichroic mirror the performance of the noise eater can be significantly improved, even with low conversion e…
Quantum memories are a crucial element towards efficient quantum protocols. In the continuous variables domain, such memories need to have near unity efficiencies. Moreover, one needs to store complex quantum states exhibiting negative Wigner functions after storage. We report the implementation of an all optical quantum memory: the storage of single and two-photon Fock states with high fidelities has been realized. The Wigner functions of the reconstructed states shows negativity after $\sim 0.75~μs$ and $\sim 0.61~μs$ respectively for the single-photon and two-photon Fock states. This is, to…
We propose a class of path-entangled photon Fock states for robust quantum optical metrology, imaging, and sensing in the presence of loss. We model propagation loss with beam-splitters and derive a reduced density matrix formalism from which we examine how photon loss affects coherence. It is shown that particular entangled number states, which contain a special superposition of photons in both arms of a Mach-Zehnder interferometer, are resilient to environmental decoherence. We demonstrate an order of magnitude greater visibility with loss, than possible with N00N states. We also show that t…
Displaced Fock states of the electromagnetic field have been synthesized by overlapping the pulsed optical single-photon Fock state |1> with coherent states on a high-reflection beamsplitter and completely characterized by means of quantum homodyne tomography. The reconstruction reveals highly non-classical properties of displaced Fock states, such as negativity of the Wigner function and photon number oscillations. This is the first time complete tomographic reconstruction has been performed on a highly non-classical optical state.
To acquire the best path-entangled photon Fock states for robust quantum optical metrology with parity detection, we calculate phase information from a lossy interferometer by using twin entangled Fock states. We show that (a) when loss is less than 50% twin entangled Fock states with large photon number difference give higher visibility while when loss is higher than 50% the ones with less photon number difference give higher visibility; (b) twin entangled Fock states with large photon number difference give sub-shot-noise limit sensitivity for phase detection in a lossy environment. This res…
Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon number distribution of a linear optical interferometric network, which is fed with single-photon Fock state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fo…
We present a scheme for the deterministic generation of N-photon Fock states from N three-level atoms in a high-finesse optical cavity. The method applies an external laser pulsethat generates an $N$-photon output state while adiabatically keeping the atom-cavity system within a subspace of optically dark states. We present analytical estimates of the error due to amplitude leakage from these dark states for general N, and compare it with explicit results of numerical simulations for N \leq 5. The method is shown to provide a robust source of N-photon states under a variety of experimental con…
The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of a new effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The …
We introduce a multi-step protocol for optical quantum state engineering that performs as deterministic "bright quantum scissors" (BQS), namely truncates an arbitrary input quantum state to have at least a certain number of photons. The protocol exploits single-photon pulses and is based on the effect of single-photon Raman interaction, which is implemented with a single three-level $Λ$ system (e.g. a single atom) Purcell-enhanced by a single-sided cavity. A single step of the protocol realises the inverse of the bosonic annihilation operator. Multiple iterations of the protocol can be used to…
Gottesman-Kitaev-Preskill (GKP) qubit is a promising ingredient for fault-tolerant quantum computation (FTQC) in optical continuous variables due to its advantage of noise tolerance and scalability. However, one of the main problems in the preparation of the optical GKP qubit is the difficulty in obtaining the nonlinearity. Cross-Kerr interaction is one of the promising candidates for this nonlinearity. There is no existing scheme to use the cross-Kerr interaction to generate the optical GKP qubit for FTQC. In this work, we propose a generation method of the GKP qubit by using a cross-Kerr int…
We propose a technique for quantum nondemolition (QND) measurement and heralded preparation of Fock states by dynamics of electromagnetically induced transparency (EIT). An atomic ensemble trapped in an optical cavity is driven by two external continuous-wave classical fields to form EIT in steady state. As soon as a weak coherent field is injected into the cavity, the EIT system departs from steady state, falls into transient state dynamics by the dispersive coupling between cavity injected photons and atoms. Because the imaginary part of time-dependent linear susceptibility Im[X(t)] of the a…
We address the design of optimal heralding schemes in linear optical quantum computing context. The problem admits unit fidelity formulation in relevant Fock space, thanks to linear optic feasibility criteria of [Phys. Rev. A100, 022301; arXiv:1901.06178]. Corresponding solution methodology is presented. As an application we inspect optimality of a few known schemes of Bell states generation. It is shown that in case of six modes and two ancillary photons success rate 2/27 is suboptimal.
Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013)]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the Hilbert space for such an interferometer and show that its dimension scales exponentially with all the physical resources. We also show in a simple example just how the Schrödinger and Heisenberg pictu…
Quantum scissors device of Pegg et al. (1998 Phys. Rev. Lett. 81, 1604) enables truncation of the Fock-state expansion of an input optical field to qubit and qutrit (three-dimensional) states only. Here, a generalized scissors device is proposed using an eight-port optical interferometer. Upon post-selection based on photon counting results, the interferometer implements generation and teleportation of qudit (d-dimensional) states by truncation of an input field at the (d-1)th term of its Fock-state expansion up to d=6. Examples of selective truncations, which can be interpreted as a Fock-stat…
Quantum receiver is an important tool for overcoming the standard quantum limit (SQL) of discrimination errors in optical communication. We theoretically study the quantum receivers for discriminating ternary and quaternary phase shift keyed coherent states in terms of average error rate and mutual information. Our receiver consists of on/off-type photon detectors and displacement operations w/o electrical feedforward operations. We show that for the ternary signals, the receiver shows a reasonable gain from the SQL even without feedforward. This scheme is realizable with the currently availab…
Single photon source is one of the key devices for optical quantum information processing. Differing from the usual stimulated Raman adiabatic passage to obtain single-photon radiation, here we propose an approach to produce optical Fock state on demand in the usual atom-cavity system by utilizing the technique of transitionless quantum driving. The present proposal effectively suppresses the unwanted but practically unavoidable nonadiabatic transitions in the previous adiabatic schemes. Therefore, the efficiency of Fock state production by the present technique could be significantly high, ev…
We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical non-linearities. Following a scheme by Bentley and Boyd [S.J. Bentley and R.W. Boyd, Optics Express 12, 5735 (2004)] we explore this effect to demonstrate interference patterns a factor of five smaller than the Rayleigh limit.
Rapid Cavity-Based Mid-Circuit Measurement and Feedforward in a Neutral Atom Array
University of California, Berkeley（加州大学伯克利分校）；Challenge Institute for Quantum Computation（量子计算挑战研究所）；Columbia University（哥伦比亚大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Fusion-based quantum computing (FBQC) offers a powerful approach to building a fault-tolerant universal quantum computer using photonic components -- single-photon sources, linear-optical circuits, single-photon detectors, and optical switching with feedforward control. Both individual optical switches and sophisticated switch networks are needed where it is necessary to perform operations conditionally, using feedforward of previous photon-detection outcomes, within the lifetime of remaining photons. Most visibly, feedforward switching is required for fault-tolerant operations at the level of…
We put forward a deterministic dissipative protocol to prepare phonon Fock states in nonlinear quantum optomechanical devices. The system is composed of a mechanical mode interacting with an optical field via radiation pressure, whereas the light mode is laser-driven in the resolved blue-sideband regime. To keep our results tractable, we have switched to an interaction picture in a displaced basis, where the effective Hamiltonian exhibits the selective photon-phonon interaction explicitly. After proper parameter adjustment and similarly to cavity-cooling schemes, the quantum evolution allows s…
An optical network of superconducting quantum bits (qubits) is an appealing platform for quantum communication and distributed quantum computing, but developing a quantum-compatible link between the microwave and optical domains remains an outstanding challenge. Operating at $T < 100$ mK temperatures, as required for quantum electrical circuits, we demonstrate a mechanically-mediated microwave-optical converter with 47$\%$ conversion efficiency, and use a feedforward protocol to reduce added noise to 38 photons. The feedforward protocol harnesses our discovery that noise emitted from the two c…
We investigate the dynamics of nonclassical states of light in coupled optical structures and we demonstrate a number of intriguing features associated with such arrangements. By diagonalizing the system's Hamiltonian, we show that these geometries can support eigenstates having anomalous optical intensity distribution with no classical counterpart. These features may provide new avenues towards manipulating light flow at the quantum level. By projecting the Hamiltonian operator on Hilbert subspaces spanning different numbers of photon excitations, we demonstrate that processes such as coheren…
The majority of linear-optical nondestructive implementations of universal quantum gates are based on single-photon resolving detectors. We propose two implementations, which are nondestructive (i.e., destroying only ancilla states) and work with conventional detectors (i.e., which do not resolve number of photons). Moreover, we analyze a recently proposed scheme of Wang et al. [J. Opt. Soc. Am. B \textbf{27}, 27 (2010)] of an optical iSWAP gate based on two ancillae in Bell's states, classical feedforward, and conventional detectors with the total probability of success equal to $η^4/32$, whe…
We demonstrate that single-photon as well as biphoton revivals are possible in a new class of dynamic optical systems-the so-called Glauber-Fock oscillator lattices. In these arrays, both Bloch-like oscillations and dynamic delocalization can occur which can be described in closed form. The bunching and anti-bunching response of path-entangled photons can be pre-engineered in such coupled optical arrangements and the possibility of emulating Fermionic behavior in this family of lattices is also considered. We elucidate these effects via pertinent examples and we discuss the prospect of experim…
We investigate the implementation of binary projective measurements with linear optics. This problem can be viewed as a single-shot discrimination of two orthogonal pure quantum states. We show that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. The statement holds in the asymptotic limit of large number of these physical resources.
We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state |1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negat…
We experimentally demonstrate the generation of multi-photon Fock states with up to three photons in well-defined spatial-temporal modes synchronized with a classical clock. The states are characterized using quantum optical homodyne tomography to ensure mode selectivity. The three-photon Fock states are probabilistically generated by pulsed spontaneous parametric down conversion at a rate of one per second, enabling complete characterization in 12 hours.
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to implement encoding circuits using passive optical devices, homodyne measurements, feedforward classical communication, conditional displacements, and off-line squeezers.
Advanced quantum technologies, as well as fundamental tests of quantum physics, crucially require the interference of multiple single photons in linear-optics circuits. This interference can result in the bunching of photons into higher Fock states, leading to a complex bosonic behaviour. These challenging tasks timely require to develop collective criteria to benchmark many independent initial resources. Here we determine whether n independent imperfect single photons can ultimately bunch into the Fock state $|n \rangle$. We thereby introduce an experimental Fock-state bunching capability for…
We discuss the spectral structure and decomposition of multi-photon states. Ordinarily `multi-photon states' and `Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of `multi-photon' states is much broader than the class of `Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an …
Post-selective attack with multi-mode projection onto Fock subspace
ITMO University（伊托莫大学）；SMARTS-Quanttelecom LLC（SMARTS-Quanttelecom有限责任公司）；Laboratory of Quantum Processes and Measurements, ITMO University（伊托莫大学量子过程与测量实验室）；Waveguide Photonics Research Center, ITMO University（伊托莫大学波导光子学研究中心）；Institute “High School of Engineering,” ITMO University（伊托莫大学高等工程学院）
Glauber-Fock lattices refer to a special class of semi-infinite tight-binding lattices with inhomogeneous hopping rates which are found in certain simple solid-state, quantum optics and quantum field theoretical models. Here it is shown that dynamic localization, i.e. suppression of quantum diffusion and periodic quantum self-imaging by an external sinusoidal force [D.H. Dunlap and V.M. Kenkre, Phys. Rev. B {\bf 34}, 3625 (1986)], can be exactly realized in Glauber-Fock lattices, in spite of inhomogeneity of hopping rates and lattice truncation.
We study a novel optical setup which is able to select a specific Fock component from a generic input state. The device allows to synthesize number states and superpositions of few number states, and to measure the photon distribution and the density matrix of a generic input signal.
The multiphoton Jaynes-Cummings model is investigated and applications in quantum information science are explored. Considering the strong atom-field coupling regime and an $N$-photon interaction, a nonlinear driving field can perform an arbitrary rotation in the Fock space of the cavity mode involving the vacuum and an $M$-Fock state, with $M<N$. Besides, driving the cavity mode with a linear coherent field (superposition of many Fock states), only the cavity states within the Fock subspace {$|0\rangle,|1\rangle,..., |N-1\rangle$} can be populated, i.e., we show how to implement a Fock state …
Heralded single photons are prepared at a rate of ~100 kHz via conditional measurements on polarization-nondegenerate biphotons produced in a periodically poled KTP crystal. The single-photon Fock state is characterized using high frequency pulsed optical homodyne tomography with a fidelity of (57.6 +- 0.1)%. The state preparation and detection rates allowed us to perform on-the-fly alignment of the apparatus based on real-time analysis of the quadrature measurement statistics.
We show that various kinds of one-photon quantum states studied in the field of quantum optics admit ladder operator formalisms and have the generally deformed oscillator algebraic structure. The two-photon case is also considered. We obtain the ladder operator formalisms of two general states defined in the even/odd Fock space. The two-photon states may also have a generally deformed oscillator algebraic structure. Some interesting examples of one-photon and two-photon quantum states are given.
The problem of on-demand generation of entanglement between single-atom qubits via a common photonic channel is examined within the framework of optical interferometry. As expected, for a Mach-Zehnder interferometer with coherent laser beam as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. We show, however, that with a twin-Fock input, useful entanglement can in principle be created without cavity-enhancement. Both approaches require single-photon resolving detectors, and best results would be obtained by combining both cavity-feedback and twi…
We propose quantum receivers with optical squeezing and photon-number-resolving detector (PNRD) for the near-optimal discrimination of quaternary phase-shift-keyed coherent state signals. The basic scheme is similar to the previous proposals (e.g. Phys. Rev. A 84, 042328 (2012)) in which displacement operations, on-off detectors, and electrical feedforward operations were used. Here we study two types of receivers where one installs optical squeezings and the other uses PNRDs instead of on-off detectors. We show that both receivers can attain lower error rates than that by the previous scheme …
Conventional Glauber coherent states (CS) can be defined in several equivalent ways, e.g., by displacing the vacuum or, explicitly, by their infinite Poissonian expansion in Fock states. It is well known that these definitions become inequivalent if applied to finite $d$-level systems (qudits). We present a comparative Wigner-function description of the qudit CS defined (i) by the action of the truncated displacement operator on the vacuum and (ii) by the Poissonian expansion in Fock states of the Glauber CS truncated at $(d-1)$-photon Fock state. These states can be generated from a classical…
We demonstrate a Fock-state filter which is capable of preferentially blocking single photons over photon pairs. The large conditional nonlinearities are based on higher-order quantum interference, using linear optics, an ancilla photon, and measurement. We demonstrate that the filter acts coherently by using it to convert unentangled photon pairs to a path-entangled state. We quantify the degree of entanglement by transforming the path information to polarisation information, applying quantum state tomography we measure a tangle of T=(20+/-9)%.
A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.
We devise a new class of criteria to certify the nonclassicality of photon- and phonon-number statistics. Our criteria extend and strengthen the broadly used Klyshko's criteria, which require knowledge of only a finite set of Fock-state probabilities. This makes the criteria well-suited to experimental implementation in realistic conditions. Moreover, we prove the completeness of our method in some scenarios, showing that, when only two or three Fock-state probabilities are known, it detects all finite distributions incompatible with classical states. In particular, we show that our criteria d…
