scispace - formally typeset
Search or ask a question

Showing papers on "Coherent states published in 2018"


Journal ArticleDOI
07 Nov 2018-Nature
TL;DR: In this article, it was shown that caesium lead halide perovskite (CsPbX3, X = Cl, Br = Br) nanocrystals exhibit key signatures of superfluorescence, such as dynamically red-shifted emission with more than 20-fold accelerated radiative decay, extension of first-order coherence time by more than a factor of four, photon bunching, and delayed emission pulses with Burnham-Chiao ringing behaviour.
Abstract: An ensemble of emitters can behave very differently from its individual constituents when they interact coherently via a common light field. After excitation of such an ensemble, collective coupling can give rise to a many-body quantum phenomenon that results in short, intense bursts of light—so-called superfluorescence1. Because this phenomenon requires a fine balance of interactions between the emitters and their decoupling from the environment, together with close identity of the individual emitters, superfluorescence has thus far been observed only in a limited number of systems, such as certain atomic and molecular gases and a few solid-state systems2–7. The generation of superfluorescent light in colloidal nanocrystals (which are bright photonic sources practically suited for optoelectronics8,9) has been precluded by inhomogeneous emission broadening, low oscillator strength, and fast exciton dephasing. Here we show that caesium lead halide (CsPbX3, X = Cl, Br) perovskite nanocrystals10–13 that are self-organized into highly ordered three-dimensional superlattices exhibit key signatures of superfluorescence. These are dynamically red-shifted emission with more than 20-fold accelerated radiative decay, extension of the first-order coherence time by more than a factor of four, photon bunching, and delayed emission pulses with Burnham–Chiao ringing behaviour14 at high excitation density. These mesoscopically extended coherent states could be used to boost the performance of opto-electronic devices15 and enable entangled multi-photon quantum light sources16,17. Cooperative quantum effects in superlattices of quantum dots made of caesium lead halide perovskite give rise to superfluorescence, with the individual emitters interacting coherently to give intense bursts of light.

361 citations


Journal ArticleDOI
TL;DR: In this article, the circuit complexity of coherent states in a free scalar field theory was examined using Nielsen's geometric approach, and the complexity of the coherent states had the same UV divergences as the vacuum state complexity.
Abstract: We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen’s geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we consider the finite increase of the complexity of these states over the vacuum state. One observation is that generally, the optimal circuits introduce entanglement between the normal modes at intermediate stages even though our reference state and target states are not entangled in this basis. We also compare our results from Nielsen’s approach with those found using the Fubini-Study method of [2]. For general coherent states, we find that the complexities, as well as the optimal circuits, derived from these two approaches, are different.

179 citations


Journal ArticleDOI
TL;DR: It is established that the one-shot distillable coherence under MIO and DIO is efficiently computable with a semidefinite program, which is shown to correspond to a quantum hypothesis testing problem.
Abstract: We characterize the distillation of quantum coherence in the one-shot setting, that is, the conversion of general quantum states into maximally coherent states under different classes of quantum operations. We show that the maximally incoherent operations (MIO) and the dephasing-covariant incoherent operations (DIO) have the same power in the task of one-shot coherence distillation. We establish that the one-shot distillable coherence under MIO and DIO is efficiently computable with a semidefinite program, which we show to correspond to a quantum hypothesis testing problem. Further, we introduce a family of coherence monotones generalizing the robustness of coherence as well as the modified trace distance of coherence, and show that they admit an operational interpretation in characterizing the fidelity of distillation under different classes of operations. By providing an explicit formula for these quantities for pure states, we show that the one-shot distillable coherence under MIO, DIO, strictly incoherent operations, and incoherent operations is equal for all pure states.

137 citations


Journal ArticleDOI
TL;DR: The concept of effective dynamics has proven successful in LQC, a loop-inspired quantization of cosmological spacetimes, by computing the expectation value of the scalar constraint with respect to some coherent states peaked on the phase-space variables of flat Robertson-Walker spacetime.

128 citations


Journal ArticleDOI
07 Feb 2018
TL;DR: In this paper, the integration of a homodyne detector onto a silicon photonics chip is described, and the resulting device operates at high speed, up 150 MHz, it is compact and it operates with low noise, quantified with 11 dB clearance between shot noise and electronic noise.
Abstract: Optical homodyne detection has found use as a characterisation tool in a range of quantum technologies. So far implementations have been limited to bulk optics. Here we present the optical integration of a homodyne detector onto a silicon photonics chip. The resulting device operates at high speed, up 150 MHz, it is compact and it operates with low noise, quantified with 11 dB clearance between shot noise and electronic noise. We perform on-chip quantum tomography of coherent states with the detector and show that it meets the requirements for characterising more general quantum states of light. We also show that the detector is able to produce quantum random numbers at a rate of 1.2 Gbps, by measuring the vacuum state of the electromagnetic field and applying off-line post processing. The produced random numbers pass all the statistical tests provided by the NIST test suite.

115 citations


Journal ArticleDOI
TL;DR: This work reports on a quantum memory for polarization qubits that combines an average conditional fidelity above 99% and efficiency around 68%, thereby demonstrating a reversible qubit mapping where more information is retrieved than lost.
Abstract: Quantum memory for flying optical qubits is a key enabler for a wide range of applications in quantum information. A critical figure of merit is the overall storage and retrieval efficiency. So far, despite the recent achievements of efficient memories for light pulses, the storage of qubits has suffered from limited efficiency. Here we report on a quantum memory for polarization qubits that combines an average conditional fidelity above 99% and efficiency around 68%, thereby demonstrating a reversible qubit mapping where more information is retrieved than lost. The qubits are encoded with weak coherent states at the single-photon level and the memory is based on electromagnetically-induced transparency in an elongated laser-cooled ensemble of cesium atoms, spatially multiplexed for dual-rail storage. This implementation preserves high optical depth on both rails, without compromise between multiplexing and storage efficiency. Our work provides an efficient node for future tests of quantum network functionalities and advanced photonic circuits.

111 citations


Journal ArticleDOI
TL;DR: The deterministic teleportation of optical modes over a 6.0-km fiber channel is realized with continuous variable entanglement and a fidelity of 0.03 for the retrieved quantum state, which breaks through the classical limit of 1/2.
Abstract: Quantum teleportation, which is the transfer of an unknown quantum state from one station to another over a certain distance with the help of nonlocal entanglement shared by a sender and a receiver, has been widely used as a fundamental element in quantum communication and quantum computation. Optical fibers are crucial information channels, but teleportation of continuous variable optical modes through fibers has not been realized so far. Here, we experimentally demonstrate deterministic quantum teleportation of an optical coherent state through fiber channels. Two sub-modes of an Einstein-Podolsky-Rosen entangled state are distributed to a sender and a receiver through a 3.0-km fiber, which acts as a quantum resource. The deterministic teleportation of optical modes over a fiber channel of 6.0 km is realized. A fidelity of 0.62 ± 0.03 is achieved for the retrieved quantum state, which breaks through the classical limit of 1/2. Our work provides a feasible scheme to implement deterministic quantum teleportation in communication networks.

95 citations


Journal ArticleDOI
TL;DR: This Letter establishes the one-shot theory of coherence dilution, which involves converting maximally coherent states into an arbitrary quantum state using maximally incoherent operations, dephasing-covariant incoherence operations, inco coherent operations, or strictly incoherent Operations.
Abstract: Manipulation and quantification of quantum resources are fundamental problems in quantum physics. In the asymptotic limit, coherence distillation and dilution have been proposed by manipulating infinite identical copies of states. In the nonasymptotic setting, finite data-size effects emerge, and the practically relevant problem of coherence manipulation using finite resources has been left open. This Letter establishes the one-shot theory of coherence dilution, which involves converting maximally coherent states into an arbitrary quantum state using maximally incoherent operations, dephasing-covariant incoherent operations, incoherent operations, or strictly incoherent operations. We introduce several coherence monotones with concrete operational interpretations that estimate the one-shot coherence cost---the minimum amount of maximally coherent states needed for faithful coherence dilution. Furthermore, we derive the asymptotic coherence dilution results with maximally incoherent operations, incoherent operations, and strictly incoherent operations as special cases. Our result can be applied in the analyses of quantum information processing tasks that exploit coherence as resources, such as quantum key distribution and random number generation.

90 citations


Journal ArticleDOI
19 Oct 2018
TL;DR: It is found that in general a quantum channel can be implemented without employing a maximally coherent resource state, and it is proved that every pure coherent state in dimension larger than 2 turns out to be a valuable resource to implement some coherent unitary channel.
Abstract: Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts. Recently, coherence has been recast as a resource theory in an attempt to identify and quantify it in an operationally well-defined manner. Here we study how the coherence present in a state can be used to implement a quantum channel via incoherent operations and, in turn, to assess its degree of coherence. We introduce the robustness of coherence of a quantum channel---which reduces to the homonymous measure for states when computed on constant-output channels---and prove that: i) it quantifies the minimal rank of a maximally coherent state required to implement the channel; ii) its logarithm quantifies the amortized cost of implementing the channel provided some coherence is recovered at the output; iii) its logarithm also quantifies the zero-error asymptotic cost of implementation of many independent copies of a channel. We also consider the generalized problem of imperfect implementation with arbitrary resource states. Using the robustness of coherence, we find that in general a quantum channel can be implemented without employing a maximally coherent resource state. In fact, we prove that \textit{every} pure coherent state in dimension larger than $2$, however weakly so, turns out to be a valuable resource to implement \textit{some} coherent unitary channel. We illustrate our findings for the case of single-qubit unitary channels.

81 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the circuit complexity of coherent states in a free scalar field theory, applying Nielsen's geometric approach as in [1] and found that the complexity of the coherent states has the same UV divergences as the vacuum state complexity and so they considered the finite increase of the complexity over the vacuum states.
Abstract: We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen's geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we consider the finite increase of the complexity of these states over the vacuum state. One observation is that generally, the optimal circuits introduce entanglement between the normal modes at intermediate stages even though our reference state and target states are not entangled in this basis. We also compare our results from Nielsen's approach with those found using the Fubini-Study method of [2]. For general coherent states, we find that the complexities, as well as the optimal circuits, derived from these two approaches, are different.

64 citations


Journal ArticleDOI
TL;DR: In this paper, an entangled state between a dual-rail (polarization-encoded) single-photon qubit and a qubit encoded as a superposition of opposite-amplitude coherent states is characterized.
Abstract: Light is an irreplaceable means of communication among various quantum information processing and storage devices. Due to their different physical nature, some of these devices couple more strongly to discrete, and some to continuous degrees of freedom of a quantum optical wave. It is therefore desirable to develop a technological capability to interconvert quantum information encoded in these degrees of freedom. Here we generate and characterize an entangled state between a dual-rail (polarization-encoded) single-photon qubit and a qubit encoded as a superposition of opposite-amplitude coherent states. We furthermore demonstrate the application of this state as a resource for the interfacing of quantum information between these encodings. In particular, we show teleportation of a polarization qubit onto a freely propagating continuous-variable qubit.

Journal ArticleDOI
TL;DR: In this paper, the authors proved that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is to minimize the decay rate of the probability of a false positive with a given probability of false negative.
Abstract: Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is to minimize the decay rate of the probability of a false positive with a given probability of a false negative. Quantum illumination with two-mode squeezed vacuum states offers a 6 dB advantage in the error probability exponent compared to illumination with coherent states. Whether more advanced quantum illumination strategies may offer further improvements had been a longstanding open question. Our fundamental result proves that nothing can be gained by considering more exotic quantum states, such as, e.g., multimode entangled states. Our proof is based on a fundamental entropic inequality for the noisy quantum Gaussian attenuators. We also prove that without access to a quantum memory, the optimal probes for quantum illumination are the coherent states.

Journal ArticleDOI
28 May 2018
TL;DR: In this article, the authors developed a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional waveguides, for example, with coherent pulsed excitation.
Abstract: We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal waveguide modes are a natural basis for characterizing scattering in quantum optics, and afford a powerful technique based on a coarse discretization of time. This overcomes limitations imposed by singularities in the waveguide-system coupling. Moreover, the integrated discretized equations can be faithfully converted to a continuous-time result by taking the appropriate limit. This approach provides a complete solution to the scattered photon field in the waveguide, and can also be used to track system-waveguide entanglement during evolution. We further develop a direct connection between quantum measurement theory and evolution of the scattered field, demonstrating the correspondence between quantum trajectories and the scattered photon state. Our method is most applicable when the number of photons scattered is known to be small, i.e. for a single-photon or photon-pair source. We illustrate two examples: analytical solutions for short laser pulses scattering off a two-level system and numerically exact solutions for short laser pulses scattering off a spontaneous parametric downconversion (SPDC) or spontaneous four-wave mixing (SFWM) source. Finally, we note that our technique can easily be extended to systems with multiple ground states and generalized scattering problems with both finite photon number input and coherent state drive, potentially enhancing the understanding of, e.g., light-matter entanglement and photon phase gates.

Journal ArticleDOI
TL;DR: In this paper, the effects of the initial photon statistics on those of the state from which the photons have been subtracted or to which they have been added are analyzed based on two closely related moment-generating functions.
Abstract: The subtraction or addition of a prescribed number of photons to a field mode does not, in general, simply shift the probability distribution by the number of subtracted or added photons. Subtraction of a photon from an initial coherent state, for example, leaves the photon statistics unchanged and the same process applied to an initial thermal state increases the mean photon number. We present a detailed analysis of the effects of the initial photon statistics on those of the state from which the photons have been subtracted or to which they have been added. Our approach is based on two closely related moment-generating functions, one that is well established and one that we introduce.

Journal ArticleDOI
TL;DR: In this paper, the Eigenstate Thermalization Hypothesis (ETH) was studied in chaotic conformal field theories (CFTs) of arbitrary dimensions and the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate.
Abstract: We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.

Journal ArticleDOI
TL;DR: Progress towards microwave quantum memories and other developments in the field of superconducting quantum devices are being used to push the limits of sensitivity of inductively-detected electron spin resonance, with prospects to scale down to even fewer spins.

Journal ArticleDOI
TL;DR: In this paper, a ternary quantum key distribution (QKD) protocol and asymptotic security proof based on three coherent states and homodyne detection is proposed.
Abstract: We introduce a ternary quantum key distribution (QKD) protocol and asymptotic security proof based on three coherent states and homodyne detection. Previous work had considered the binary case of two coherent states and here we nontrivially extend this to three. Our motivation is to leverage the practical benefits of both discrete and continuous (Gaussian) encoding schemes creating a best-of-both-worlds approach; namely, the postprocessing of discrete encodings and the hardware benefits of continuous ones. We present a thorough and detailed security proof in the limit of infinite signal states which allows us to lower bound the secret key rate. We calculate this is in the context of collective eavesdropping attacks and reverse reconciliation postprocessing. Finally, we compare the ternary coherent state protocol to other well-known QKD schemes (and fundamental repeaterless limits) in terms of secret key rates and loss.

Journal ArticleDOI
TL;DR: In this paper, the information-theoretic aspects of the infrared sector of quantum electrodynamics were studied using the dressed-state approach pioneered by Chung, Kibble, Faddeev-Kulish, and others.
Abstract: We study information-theoretic aspects of the infrared sector of quantum electrodynamics, using the dressed-state approach pioneered by Chung, Kibble, Faddeev-Kulish, and others. In this formalism QED has an IR-finite S-matrix describing the scattering of electrons dressed by coherent states of photons. We show that measurements sensitive only to the outgoing electronic degrees of freedom will experience decoherence in the electron momentum basis due to unobservable photons in the dressing. We make some comments on possible refinements of the dressed-state formalism, and how these considerations relate to the black hole information paradox.

Journal ArticleDOI
TL;DR: In this article, the robustness of coherence of a quantum channel was studied and the authors showed that every pure coherent state in dimension larger than 2, however weakly so, turns out to be a valuable resource to implement some coherent unitary channel.
Abstract: Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts. Recently, coherence has been recast as a resource theory in an attempt to identify and quantify it in an operationally well-defined manner. Here we study how the coherence present in a state can be used to implement a quantum channel via incoherent operations and, in turn, to assess its degree of coherence. We introduce the robustness of coherence of a quantum channel---which reduces to the homonymous measure for states when computed on constant-output channels---and prove that: i) it quantifies the minimal rank of a maximally coherent state required to implement the channel; ii) its logarithm quantifies the amortized cost of implementing the channel provided some coherence is recovered at the output; iii) its logarithm also quantifies the zero-error asymptotic cost of implementation of many independent copies of a channel. We also consider the generalized problem of imperfect implementation with arbitrary resource states. Using the robustness of coherence, we find that in general a quantum channel can be implemented without employing a maximally coherent resource state. In fact, we prove that \textit{every} pure coherent state in dimension larger than $2$, however weakly so, turns out to be a valuable resource to implement \textit{some} coherent unitary channel. We illustrate our findings for the case of single-qubit unitary channels.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the harvesting of entanglement and mutual information by Unruh-DeWitt particle detectors from thermal and squeezed coherent field states, and showed that the harvesting ability of detectors decreases monotonically with the field temperature T, harvested mutual information grows linearly with T.
Abstract: We study the harvesting of entanglement and mutual information by Unruh-DeWitt particle detectors from thermal and squeezed coherent field states. We prove (for arbitrary spatial dimensions, switching profiles and detector smearings) that while the entanglement harvesting ability of detectors decreases monotonically with the field temperature T, harvested mutual information grows linearly with T. We also show that entanglement harvesting from a general squeezed coherent state is independent of the coherent amplitude, but depends strongly on the squeezing amplitude. Moreover, we find that highly squeezed states (i) allow for detectors to harvest much more entanglement than from the vacuum, and (ii) ensure that the entanglement harvested does not decay with their spatial separation. Finally, we analyze the spatial inhomogeneity of squeezed states and its influence on harvesting, and investigate how much entanglement one can actually extract from squeezed states when the squeezing is bandlimited.

Journal ArticleDOI
20 May 2018
TL;DR: In this paper, the authors reported on quantum frequency conversion of memory-compatible narrow-bandwidth photons at 606-nm to the telecom C-band at 1552-nm using a periodically poled lithium niobate waveguide.
Abstract: The coherent manipulation of the frequency of single photons is an important requirement for future quantum network technologies. It allows, for instance, quantum systems emitting in the visible range to be connected to the telecommunication wavelengths, thus extending the communication distances. Here we report on quantum frequency conversion of memory-compatible narrow-bandwidth photons at 606 nm to the telecom C-band at 1552 nm. The 200 ns long photons, compatible with praseodymium-based solid-state quantum memories, are frequency converted using a single-step difference frequency-generation process in a periodically poled lithium niobate waveguide. We characterize the noise processes involved in the conversion and, by applying strong spectral filtering of the noise, we demonstrate high signal-to-noise ratio conversion at the single-photon level (SNR>100, for a mean input photon number per pulse of 1). We finally observe that a memory-compatible heralded single photon with a bandwidth of 1.8 MHz, obtained from a spontaneous parametric down-conversion pair source, still shows a strong non-classical behavior after conversion. We first demonstrate that correlations between heralding and converted heralded photons stay in the non-classical regime. Moreover, we measure the heralded autocorrelation function of the heralded photon using the converter device as a frequency-domain beam splitter, yielding a value of 0.19±0.07. The presented work represents a step towards the connection of several quantum memory systems emitting narrowband visible photons to the telecommunication wavelengths.

Journal ArticleDOI
TL;DR: In this article, the authors extended this approach to the case of a single trapped ion and showed improved sensitivity to changes in the oscillator frequency, with the maximal value at $n=12 dB higher sensitivity compared to an ideal measurement on a coherent state with the same average occupation number.
Abstract: The use of special quantum states to achieve sensitivities below the limits established by classically behaving states has enjoyed immense success since its inception. In bosonic interferometers, squeezed states, number states and cat states have been implemented on various platforms and have demonstrated improved measurement precision over interferometers based on coherent states. Another metrologically useful state is an equal superposition of two eigenstates with maximally different energies; this state ideally reaches the full interferometric sensitivity allowed by quantum mechanics. By leveraging improvements to our apparatus made primarily to reach higher operation fidelities in quantum information processing, we extend a technique to create number states up to $n=100$ and to generate superpositions of a harmonic oscillator ground state and a number state of the form $\textstyle{\frac{1}{\sqrt{2}}}(\lvert 0\rangle+\lvert n\rangle)$ with $n$ up to 18 in the motion of a single trapped ion. While experimental imperfections prevent us from reaching the ideal Heisenberg limit, we observe enhanced sensitivity to changes in the oscillator frequency that initially increases linearly with $n$, with maximal value at $n=12$ where we observe 3.2(2) dB higher sensitivity compared to an ideal measurement on a coherent state with the same average occupation number. The quantum advantage from using number-state superpositions can be leveraged towards precision measurements on any harmonic oscillator system; here it enables us to track the average fractional frequency of oscillation of a single trapped ion to approximately 2.6 $\times$ 10$^{-6}$ in 5 s. Such measurements should provide improved characterization of imperfections and noise on trapping potentials, which can lead to motional decoherence, a leading source of error in quantum information processing with trapped ions.

Journal ArticleDOI
TL;DR: A strategy for binary state discrimination based on optimized single-shot measurements with photon number resolving detection with a finite number resolution is demonstrated, enabling a high degree of robustness to noise and imperfections while being scalable to high rates and allowing for surpassing the quantum noise limit in practical situations.
Abstract: The discrimination of two nonorthogonal states is a fundamental element for secure and efficient communication Quantum measurements of nonorthogonal coherent states can enhance information transfer beyond the limits of conventional technologies We demonstrate a strategy for binary state discrimination based on optimized single-shot measurements with photon number resolving detection with a finite number resolution This strategy enables a high degree of robustness to noise and imperfections while being scalable to high rates and, in principle, allows for surpassing the quantum noise limit (QNL) in practical situations These features make the strategy inherently compatible with high-bandwidth communication and quantum information applications, providing advantages over the QNL under realistic conditions

Journal ArticleDOI
TL;DR: In this article, a set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied and two different nonlinear algebras generated by properly constructed ladder operators are found and corresponding generalized coherent states are obtained.

Journal ArticleDOI
TL;DR: In this article, the motional state of a mechanical oscillator was obtained by adding a single phonon to the coherent state via parametric down-conversion combined with single-photon detection.
Abstract: Adding excitations on a coherent state provides an effective way to observe the nonclassical properties of radiation fields. Here, we describe and analyze how to apply this concept to the motional state of a mechanical oscillator and present a full scheme to prepare non-Gaussian phonon-added coherent states of the mechanical motion in cavity optomechanics. We first generate a mechanical coherent state using electromagnetically induced transparency. We then add a single phonon onto the coherent state via optomechanical parametric down-conversion combined with single-photon detection. We validate this single-phonon-added coherent state by using a red-detuned beam and reading out the state of the optical output field. This approach allows us to verify nonclassical properties of the phonon state, such as sub-Poissonian character and quadrature squeezing. We further show that our scheme can be directly implemented using existing devices, and is generic in nature and hence applicable to a variety of systems in opto- and electromechanics.

Journal ArticleDOI
TL;DR: The results show that the phase sensitivity of an SU(1,1) interferometer reaches the sub-shot-noise limit with a coherent state and an m-photon-added squeezed vacuum state (m-PA-SVS) as inputs.
Abstract: We study the phase sensitivity of an SU(1,1) interferometer from two aspects, i.e., the phase estimation determined by the error propagation formula and that by the quantum Cramer-Rao bound (QCRB). The results show that the phase sensitivity by using the intensity detection reaches the sub-shot-noise limit with a coherent state and an m-photon-added squeezed vacuum state (m-PA-SVS) as inputs. The phase sensitivity gradually approaches the Heisenberg limit for increasing m, and the ultimate phase precision improves with the increase of m. In addition, the QCRB can be saturated by the intensity detection with inputting the m-PA-SVS.

Journal ArticleDOI
TL;DR: In this paper, the basic mechanisms and general conditions for the emergence of Bellerophon states appearing in globally coupled phase oscillators are revealed, and critical points for the involved phase transitions are determined analytically.
Abstract: We unveil the basic mechanisms and general conditions for the emergence of Bellerophon states, which are higher order coherent states appearing in globally coupled phase oscillators. The critical points for the involved phase transitions are determined analytically. The significant feature of Bellerophon states is that the oscillators' effective frequencies are locked to quantized plateaus, a point which is fully clarified on the basis of circle map theory. Each quantized plateau corresponds to a harmonic frequency of the Fourier decomposition of the order parameter. Our approach exploits the fact that the order parameter is always real, due to a special symmetry of the system which furthermore prevents the formation of even integer multiple plateaus of effective frequencies.


Journal ArticleDOI
TL;DR: The Leggett-Garg inequality can be violated through a genuine negative result measurement, thereby repudiating the everyday notion of macrorealism and opening up potentially the simplest way for testing whether various recently engineered and sought after macroscopic oscillators are indeed bona fide nonclassical objects.
Abstract: Can the most ``classical-like'' of all quantum states, namely the Schr\"odinger coherent state of a harmonic oscillator, exhibit nonclassical behavior? We find that for an oscillating object initially in a coherent state, merely by observing at various instants which spatial region the object is in, the Leggett-Garg inequality (LGI) can be violated through a genuine negative result measurement, thereby repudiating the everyday notion of macrorealism. This violation thus reveals an unnoticed nonclassicality of the very state which epitomizes classicality within the quantum description. It is found that for any given mass and oscillator frequency, a significant quantum violation of LGI can be obtained by suitably choosing the initial peak momentum of the coherent state wave packet. It thus opens up potentially the simplest way (without coupling with any ancillary quantum system or using nonlinearity) for testing whether various recently engineered and sought after macroscopic oscillators, such as feedback cooled thermal trapped nanocrystals of $\ensuremath{\sim}{10}^{6}--{10}^{9}\text{ }\text{ }\mathrm{amu}$ mass, are indeed bona fide nonclassical objects.

Journal ArticleDOI
TL;DR: Security analysis shows that the proposed scheme can lengthen the maximum transmission distance up to hundreds of kilometers, and by taking finite-size effect and composable security into account the authors obtain the tightest bound of the secure distance, which is more practical than that obtained in the asymptotic limit.
Abstract: We propose a long-distance continuous-variable quantum key distribution (CVQKD) with a four-state protocol using non-Gaussian state-discrimination detection. A photon subtraction operation, which is deployed at the transmitter, is used for splitting the signal required for generating the non-Gaussian operation to lengthen the maximum transmission distance of the CVQKD. Whereby an improved state-discrimination detector, which can be deemed as an optimized quantum measurement that allows the discrimination of nonorthogonal coherent states beating the standard quantum limit, is applied at the receiver to codetermine the measurement result with the conventional coherent detector. By tactfully exploiting the multiplexing technique, the resulting signals can be simultaneously transmitted through an untrusted quantum channel, and subsequently sent to the state-discrimination detector and coherent detector, respectively. Security analysis shows that the proposed scheme can lengthen the maximum transmission distance up to hundreds of kilometers. Furthermore, by taking the finite-size effect and composable security into account we obtain the tightest bound of the secure distance, which is more practical than that obtained in the asymptotic limit.