Homodyne Measurement Research Articles

Photonic hybrid state entanglement swapping using cat state superpositions.

We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state super- position) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of , when used with a suitable entanglement purification scheme.

Generation of an arbitrary logic W state with cross-Kerr nonlinearities

Environmental noise is a big obstacle in quantum communication and computation. Quantum error code (QEC) technology can resist the photon transmission loss and decoherence error caused by the environmental noise and has great application potential in future quantum communication and computation fields. The generation of logic qubits or logic entanglement is the important first step of the QEC. The logic W state, which replaces each physical qubit in a physical W state with a logic qubit, may be highly robust against photon loss and errors, so that it may have big application potential. In this paper, we propose an efficient scheme to generate an arbitrary logic W state with the help of cross-Kerr nonlinearities. Our protocol only requires a physical W state and some auxiliary single photons, and can deterministically generate a general logic W state based on the homodyne measurement results. Our logic W state generation protocol may be useful in future quantum information processing based on the logic W state.

Design of an on-Chip Room Temperature Group-IV Quantum Photonic Chem/Bio Interferometric Sensor Based on Parity Detection.

We propose and analyze three Si-based room-temperature strip-guided “manufacturable” integrated quantum photonic chem/bio sensor chips operating at wavelengths of 1550 nm, 1330 nm, and 640 nm, respectively. We propose design rules that will achieve super-sensitivity (above the classical limit) by means of mixing between states of coherent light and single-mode squeezed-light. The silicon-on-insulator (SOI), silicon-on-sapphire (SOS), and silicon nitride-on-SiO2-on Si (SiN) platforms have been investigated. Each chip is comprised of photonic building blocks: a race-track resonator, a pump filter, an integrated Mach-Zehnder interferometric chem/bio sensor, and a photonic circuit to perform parity measurements, where our homodyne measurement circuit avoids the use of single-photon-counting detectors and utilizes instead conventional photodetectors. A combination of super-sensitivity with super-resolution is predicted for all three platforms to be used for chem/bio sensing applications.

Distillation of squeezing using an engineered pulsed parametric down-conversion source.

Hybrid quantum information processing combines the advantages of discrete and continues variable protocols by realizing protocols consisting of photon counting and homodyne measurements. However, the mode structure of pulsed sources and the properties of the detection schemes often require the use of optical filters in order to combine both detection methods in a common experiment. This limits the efficiency and the overall achievable squeezing of the experiment. In our work, we use photon subtraction to implement the distillation of pulsed squeezed states originating from a genuinely spatially and temporally single-mode parametric down-conversion source in non-linear waveguides. Due to the distillation, we witness an improvement of 0.17 dB from an initial squeezing value of -1.648 ± 0.002 dB, while achieving a purity of 0.58, and confirm the non-Gaussianity of the distilled state via the higher-order cumulants. With this, we demonstrate the source's suitability for scalable hybrid quantum network applications with pulsed quantum light.

Quantum-Enhanced Fiber-Optic Gyroscopes Using Quadrature Squeezing and Continuous-Variable Entanglement

We evaluate the fundamental performance of a fiber-optic gyroscope (FOG) design that is enhanced by the injection of a quantum-optical squeezed vacuum. In the presence of fiber loss, we compute the optimum attainable enhancement below the standard quantum limit in terms of the angular velocity estimator variance from a homodyne measurement. We find that currently realizable amounts of single-mode squeezing are sufficient to access the maximum quantitative improvement, but that this gain in maximum rotation sensitivity is limited to a marginal constant factor. We then propose an entanglement-enhanced FOG design that segments a fixed amount of available fiber into multiple fiber interferometers and feeds this sensor array with a multimode-entangled squeezed vacuum resource. Our design raises the fundamental improvement in sensitivity to an appreciable factor of $e\ensuremath{\approx}2.718$.

Effective discrimination of chiral molecules in a cavity.

We present a scheme to realize precise discrimination of chiral molecules in a cavity. Assisted by additional laser pulses, cavity fields can evolve into different coherence states with contrary-sign displacements according to the handedness of molecules. Consequently, the handedness of molecules can be read out with homodyne measurement on the cavity, and the successful probability is nearly unity without very strong cavity fields. Numerical results show that the scheme is insensitive to errors, noise, and decoherence. Therefore, the scheme may provide helpful perspectives for accurate discrimination of chiral molecules.

Generating entangled Schrödinger cat states using a number state and a beam splitter

Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrodinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [M. Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order.

Schrödinger cat states in continuous variable non-Gaussian networks

We show how continuous variable network with embedded non-Gaussian element can effectively prepare Schrödinger cat state using cubic phase state as elementary non-Gaussian resource, an entangling Gaussian gate, and homodyne measurement. The gate prepares superposition of two “copies” of an arbitrary input state well separated on the phase plane. A key feature of the cat-breeding configuration is that the measurement outcome provides multivalued information about the target system variables, which makes irrelevant the Heisenberg picture as it is applied to Gaussian networks. We present an intuitively clear interpretation of the emerging cat state, extendable to the circuits with other non-Gaussian elements.

Spectral Evidence of Squeezing of a Weakly Damped Driven Nanomechanical Mode

Because of the broken time-translation symmetry, in periodically driven vibrational systems fluctuations of different vibration components have different intensities. Fluctuations of one of the components are often squeezed, whereas fluctuations of the other component, which is shifted in phase by {\pi}/2, are increased. Squeezing is a multifaceted phenomenon; it attracts much attention from the perspective of high-precision measurements. Here we demonstrate a new and hitherto unappreciated side of squeezing: its direct manifestation in the spectra of driven vibrational systems. With a weakly damped nanomechanical resonator, we study the spectrum of thermal fluctuations of a resonantly driven nonlinear mode. In the attained sideband-resolved regime, we show that the asymmetry of the spectrum directly characterizes the squeezing. This opens a way to deduce squeezing of thermal fluctuations in strongly underdamped resonators, for which a direct determination by a standard homodyne measurement is impeded by frequency fluctuations. The experimental and theoretical results are in excellent agreement. We further extend the theory to also describe the spectral manifestation of squeezing of quantum fluctuations.

Generating mechanical and optomechanical entanglement via pulsed interaction and measurement

Entanglement generation at a macroscopic scale offers an exciting avenue to develop new quantum technologies and study fundamental physics on a tabletop. Cavity quantum optomechanics provides an ideal platform to generate and exploit such phenomena owing to the precision of quantum optics combined with recent experimental advances in optomechanical devices. In this work, we propose schemes operating outside the resolved-sideband regime, to prepare and verify both optical–mechanical and mechanical–mechanical entanglement. Our schemes employ pulsed interactions with a duration much less than the mechanical period and, together with homodyne measurements, can both generate and characterize these types of entanglement. To improve the performance of our schemes, a precooling stage comprising prior pulses can be utilized to increase the amount of entanglement prepared, and local optical squeezers may be used to provide resilience against open-system dynamics. The entanglement generated by our schemes is quantified using the logarithmic negativity and is analysed with respect to the strength of the pulsed optomechanical interactions for realistic experimental scenarios including mechanical decoherence and optical loss. Two separate schemes for mechanical entanglement generation are introduced and compared: one scheme based on an optical interferometric design, and the other comprising sequential optomechanical interactions. The pulsed nature of our protocols provides more direct access to these quantum correlations in the time domain, with applications including quantum metrology and tests of quantum decoherence. By considering a parameter set based on recent experiments, the feasibility to generate significant entanglement with our schemes, even with large optical losses, is demonstrated.

Switchable bipartite and genuine tripartite entanglement via an optoelectromechanical interface

Controllable multipartite entanglement is a crucial element in quantum information processing. Here we present a scheme that generates switchable bipartite and genuine tripartite entanglement between microwave and optical photons via an optoelectromechanical interface, where microwave and optical cavities are coupled to a mechanical mode with controllable coupling constants. We show that by tuning an effective gauge phase between the coupling constants to the "sweet spots", bipartite entanglement can be generated and switched between designated output photons. The bipartite entanglement is robust against the mechanical noise and the signal loss to the mechanical mode when the couplings are chosen to satisfy the impedance matching condition. When the gauge phase is tuned away from the "sweet spots", genuine tripartite entanglement can be generated and verified with homodyne measurement on the quadratures of the output fields. Our result can lead to the implementation of controllable and robust multipartite entanglement in hybrid quantum systems operated in distinctively different frequencies.

Multimode single-pass spatio-temporal squeezing.

We present a single-pass source of broadband multimode squeezed light with potential application in quantum information and quantum metrology. The source is based on a type I parametric down-conversion (PDC) process inside a bulk nonlinear crystal in a non-collinear configuration. The generated squeezed light exhibits a spatio-temporal multimode behavior that is probed using a homodyne measurement with a local oscillator shaped both spatially and temporally. Finally we follow a covariance matrix based approach to reveal the distribution of the squeezing among several independent temporal and spatial modes. This unambiguously validates the multimode feature of our source.

Pulsed atom-mechanical quantum non-demolition gate

Hybridization of quantum science and technology crucially depends on quantum gates between various physical systems. The different platforms have different fundamental physics and, therefore, diverse advantages in various applications. Many applications require nearly ideal quantum gates with variable large interaction gain and sufficient entangling power. Moreover, pulsed gates are advantageous for fast quantum circuits. For quantum systems with continuous variables, the quantum non-demolition (QND) gate is the most basic. It is an entangling gate that simultaneously keeps a variable of the interacting system unchanged. This feature is useful for quantum circuits from quantum sensing to continuous variable quantum computing. Currently, atomic ensembles storing quantum states of radiation and mechanical oscillators transducing them are two major but very different continuous-variable matter platforms. We propose a high-quality continuous-variable QND gate between an atomic ensemble and a mechanical oscillator in the separated optical cavities connected by propagating optical pulses. We demonstrate that squeezing of light pulses, homodyne measurement, and optimized feedforward control used to build the gate are sufficient to reach an interaction gain up to 50 with nearly ideal entangling power.

Accurate photonic temporal mode analysis with reduced resources

The knowledge and thus characterization of the temporal modes of quantum light fields is important in many areas of quantum physics ranging from experimental setup diagnosis to fundamental-physics investigations. Recent results showed how the auto-correlation function computed from continuous-wave homodyne measurements can be a powerful way to access the temporal mode structure. Here, we push forward this method by providing a deeper understanding and by showing how to extract the amplitude and phase of the temporal mode function with reduced experimental resources. Moreover, a quantitative analysis allows us to identify a regime of parameters where the method provides a trustworthy reconstruction, which we illustrate experimentally.

The Phase Sensitivities for Different Phase-Shift Configurations in an SU(1,1) Interferometer**Supported by the National Natural Science Foundation of China under Grant Nos. 11747161 and 11974189 and the China Postdoctoral Science Foundation under Grant No. 2018M642293

We theoretically study the phase sensitivities of two different phase-shift configurations in an SU(1,1) interferometer with coherent ⊗ squeezed vacuum states. According to quantum Cramér-Rao theorem, we analytically obtain the ultimate phase sensitivities for two types of phase shift accumulating in one- and two-arm. Compared with the case of one-arm phase shift, the model with phase shift encoding in both arms may provide a better sensitivity when the strength of squeezed vacuum state is large enough. Furthermore, we discuss the achievable sensitivities with the homodyne measurement by invoking of error-propagation formula. In addition, we study the effect of internal and outernal photon losses on the phase sensitivity of the SU(1,1) interferometer and find that the unbalanced interferometer is helpful to improve precision even with high external losses.

Conversion of Knill–Laflamme–Milburn Entanglement to Greenberger–Horne–Zeilinger Entanglement

AbstractSchemes for converting photonic polarized‐entangled Knill–Laflamme–Milburn (KLM) states to Greenberger–Horne–Zeilinger (GHZ) states are proposed using weak cross‐Kerr nonlinearity and X‐quadrature homodyne measurement. Analyses show that the two‐qubit (Bell state) and three‐qubit conversion cases have very high fidelities and close‐to‐unity probabilities. The conversion processes are robust against photon loss. The schemes linking these two entangled states may be helpful to the study of quantum information processing based on them.

Quantum state preparation of an atomic ensemble via cavity-assisted homodyne measurement

The quantum spin states of an atomic ensemble are of special interest to both fundamental studies and precision measurement applications. Here, we propose a scheme to prepare collective quantum states of an atomic ensemble placed in an optical cavity via homodyne measurement of a probing light field. The effective interactions of atoms mediated by photons are enhanced by the optical cavity, and the output probe light could also be entangled with the collective spin states. By selectively measuring the quadrature of the output light, we can prepare various quantum states, including superposition states of Dicke states and Dicke squeezed states. It is also demonstrated that the fidelity of the prepared quantum state can be enhanced by repetitive homodyne detection and using longer probe laser pulses. With the experimental parameters, we discuss some imperfections, including background noise, fluctuation of the measurement outcomes, and free-space scattering.We believe that our scheme should be feasible for experimental realization with current technologies, which may be used in the future study of quantum mechanics and quantum metrology.

Self referencing attosecond interferometer with zeptosecond precision.

In this work we demonstrate the generation of two intense, ultrafast laser pulses that allow a controlled interferometric measurement of higher harmonic generation pulses with 12.8 attoseconds in resolution (half the atomic unit of time) and a precision as low as 680 zeptoseconds (10-21 seconds). We create two replicas of a driving femtosecond pulse which share the same optical path except at the focus where they converge to two foci. An attosecond pulse train emerges from each focus through the process of high harmonic generation. The two attosecond pulse trains from each focus interfere in the far field producing a clear interference pattern in the extreme ultraviolet region. By controlling the relative optical phase (carrier envelope phase for pulsed fields) between the two driving laser pulses we are able to actively influence the delay between the pulses and are able to perform very stable and precise pump-probe experiments. Because of the phase shaping operation occurs homogeneously across the entire spatial profile, we effectively create two indistinguishable intense laser pulses or a common path interferometer for attosecond pulses. Commonality across the two beams means that they are extremely stable to environmental and mechanical fluctuations up to a Rayleigh range from the focus. In our opinion this represents an ideal source for homodyne and heterodyne spectroscopic measurements with sub-attosecond precision.

The Estimation Lie Algebra Associated with Quantum Filters

We introduce the Lie algebra of super-operators associated with a quantum filter, specifically emerging from the Stratonovich calculus. In classical filtering, the analogue algebra leads to a geometric theory of nonlinear filtering which leads to well-known results by Brockett and by Mitter characterizing potential models where the curse-of-dimensionality may be avoided, and finite dimensional filters obtained. We discuss the quantum analogue to these results. In particular, we see that, in the case where all outputs are subjected to homodyne measurement, the Lie algebra of super-operators is isomorphic to a Lie algebra of system operators from which one may approach the question of the existence of finite-dimensional filters.

High-fidelity bosonic quantum state transfer using imperfect transducers and interference

We consider imperfect two-mode bosonic quantum transducers that cannot completely transfer an initial source-system quantum state due to insufficient coupling strength or other Hamiltonian non-idealities. We show that such transducers can generically be made perfect by using interference and phase-sensitive amplification. Our approach is based on the realization that a particular kind of imperfect transducer (one which implements a swapped quantum non-demolition (QND) gate) can be made into a perfect one-way transducer using feed-forward and/or injected squeezing. We show that a generic imperfect transducer can be reduced to this case by repeating the imperfect transduction operation twice, interspersed with amplification. Crucially, our scheme only requires the ability to implement squeezing operations and/or homodyne measurement on one of the two modes involved. It is thus ideally suited to schemes where there is an asymmetry in the ability to control the two coupled systems (e.g., microwave-to-optics quantum state transfer). We also discuss a correction protocol that requires no injected squeezing and/or feed-forward operation.