The frequency comb of a multimode interferometer offers exceptional scalability potential for field-encoded quantum information. However, the staple field detection method, homodyne detection, cannot access quantum information in the whole comb because some spectral quadratures [and their asymmetries with respect to the local oscillator (LO)] are out of reach. We present here the first general approach to making optimal measurements of a multimode quantum optical source—something that is required for photonic quantum computing and is not possible when using homodyne detection with a pulse-shaped LO. This approach uses universal spectral mode-matching, which can be understood as interferometry with a memory effect. We derive a complete formalism and propose an implementation by microcavity arrays.
The frequency comb of a multimode interferometer offers exceptional scalability potential for field-encoded quantum information. However, the staple field detection method, homodyne detection, cannot access quantum information in the whole comb because some spectral quadratures [and their asymmetries with respect to the local oscillator (LO)] are out of reach. We present here the first general approach to making optimal measurements of a multimode quantum optical source—something that is required for photonic quantum computing and is not possible when using homodyne detection with a pulse-shaped LO. This approach uses universal spectral mode-matching, which can be understood as interferometry with a memory effect. We derive a complete formalism and propose an implementation by microcavity arrays.
The fields of precision timekeeping and spectroscopy increasingly rely on optical-frequency-comb interferometry. However, comb-based measurements are not described by existing quantum theory because they exhibit both large mode mismatch and finite-strength local oscillators. To establish this quantum theory, we derive measurement operators for homodyne detection with arbitrary mode overlap. These operators are a combination of quadrature and intensity-like measurements, which inform a filter that maximizes the quadrature-measurement signal-to-noise ratio. Furthermore, these operators establish a foundation to extend frequency-comb interferometry to a wide range of scenarios, including metrology with nonclassical states of light.
Summary form only given. Optical techniques are widely used in many areas of science and technology to make accurate measurements. The precision of these measurements suffers from limits due to the unavoidable quantum fluctuations of light. When the light is in the quasi-classical coherent state, this limit is called ”standard quantum limit” and scales as 1/√N with N the number of photons. While better scaling can be achieved with exotic quantum states, coherent light is experimentally interesting as we are able to produce it with large N. We consider light as a probe for the measurement of a parameter p that affects the medium or the length through which the light propagates. We derived the ultimate limit of sensitivity, the so-called quantum Cramér-Rao bound, for the measurement of p [1]: for u(ω, p) the normalized mean field mode of the light, the minimal fluctuation of p that can be measured is given in Fig. 1. We also showed that this ultimate limit of sensitivity can be reached experimentally in a homodyne detection scheme, where the intense local oscillator is taken in the mode wp o ∂u ∂p, called detection mode associated with p. This measurement scheme can be applied to space-time positioning experiments such as ranging or clock synchronization [2]. The basic method for space-time positioning relies on the exchange of regular light pulses between two emitters. For coherent broadband light pulses, such as the ones delivered by a mode-locked femtosecond laser, of central frequency ω0 and of spectral width Δω, the quantum limits of the measurements of the delay t are given by δtphase = 2√Nω0 1 for interferometric measurements and δttof = 2√NΔω 1 for time-of-flight measurements. However, these two methods do not reach the quantum Cramer-Rao bound; this ultimate limit is achieved by a homodyne detection with local oscillator w(ω) o iωu(ω), and is given by 1 δtmin = (1) 2√N . Δω2 + ω2 0 For usual characteristics of a Titane:Sapphire femtosecond laser and 1 ms integration time, δtmin = 10-23s. We demonstrate this limit experimentally by using pulse shaping techniques to shape the local oscillator in the detection mode. We also study the influence of the intensity and phase noise of a mode-locked femtosecond laser on this limit. This technique can also be applied in the case of ranging in a dispersive medium such as air. In this case, dispersive effects due to environmental parameters such as pressure, temperature or humidity affect the precision of measurements. Usually, this problem is tacked by measuring separately the environmental parameters or using several wavelengths, which can be difficult and require post-processing. We show that using the same technique as previously shown, the parasitic effects due to the medium in a distance measurement can be canceled by shaping properly the local oscillator [3]: we choose for the local oscillator a mode that is orthogonal to the environmental effects, so the homodyne detection is insensitive to them, at the expense of a lower sensitivity. This scheme is an all-optical and real-time measurement of distance in a dispersive medium.
Recently, continuous variables (CV) quantum computing, i. e. computing employing squeezed states, has attracted significant attention, as it enables to increase the dimensionality of the system. In CV protocols, homodyne detection plays a key role in the realization of the required gates and operations. Multimode squeezed light generated via parametric down-conversion (PDC) benefits from the broadband bandwidth, which encompasses multiple frequency modes. However, its broadband structure simultaneously requires the precise matching of the local oscillator (LO) with the squeezed light modes for their correct homodyne detection and processing. Achieving such matching is usually a challenging task, since the spectral bandwidth of the local oscillator is typically significantly narrower than the bandwidth of the squeezed-light modes. In this work, we propose and experimentally demonstrate a technique for expanding the bandwidth of the LO by passing it through the microstructured fiber. We validate the proposed concept by measuring squeezing in the modes of multimode squeezed light generated in type-0 and type-II PDC. We show that the broadened LO starts to spectrally match the modes generated via type-II PDC. The presented technique might be beneficial for implementing various CV systems and protocols.
One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a scalable method that uses a single, multimode optical parametric oscillator (OPO). The method is very efficient and generates a continuous-variable cluster state, universal for quantum computation, with quantum information encoded in the quadratures of the optical frequency comb of the OPO.
Abstract Measuring the spectral properties of an optical frequency comb is among the most fundamental tasks of precision metrology. In contrast to general single-parameter measurement schemes, we demonstrate here single shot multi-parameter estimation of an optical frequency comb at and beyond the standard quantum limit. The mean energy and the central frequency as well as the spectral bandwidth of ultrafast pulses are simultaneously determined with a multi-pixel spectrally resolved (MPSR) apparatus, without changing the photonics architecture. Moreover, using a quantum frequency comb that intrinsically consists of multiple squeezed states in a family of Hermite–Gaussian spectral/temporal modes, the signal-to-noise ratios of the multiple spectral parameters estimation can surpass the standard quantum limit. Combining our multi-pixel detection scheme and the multimode entangled resource could find applications in ultrafast quantum metrology and multimode quantum information processing.
Optical Gaussian entangled states can be generated deterministically, up to very large number of modes. Furthermore, for nontrivial quantum computation, non-Gaussianity is required, which can be obtained from photon subtraction. We will explore here the controlled generation of multimode graph states from ultrafast optical pulses (optical frequency combs) and parametric down conversion in a synchronously pumped cavity, investigating in particular spectral shaping of the pump. Mode dependent photon subtraction is then implemented through sum-frequency generation, and characterization is performed through frequency resolved homodyne detection. We study the influence of a non Gaussian ingredient on a Gaussian graph state.