This study addresses any sensor based on measuring a physical quantity through the phase of a probing beam. This includes sensing of rotation, acceleration, index change, displacement, fields… While most phase measurements are made by detecting an amplitude change in interfering beams, we detect instead a phase change through a relative frequency shift of two correlated frequency combs. This paper explores the limit sensitivity that this method can achieve, when the combs are generated in an Optical Parametric Oscillator (OPO), pumped synchronously by a train of femtosecond pulses separated by half the OPO cavity round-trip time. It is shown that a phase difference as small as 0.4 nanoradians can be resolved between the two pulses circulating in the cavity. This phase difference is one order of magnitude better than the previous record. The root-mean-square deviation of the measured phase over measuring time is close to the standard quantum limit (phase-photon number uncertainty product of 0.66). Innovations that made such improved performances possible include a more stable OPO cavity design; a stabilization system with a novel purely electronic locking of the OPO cavity length relative to that of the pump laser; a shorter pump laser cavity; and a square pulse generator for driving a 0.5 mm pathlength lithium niobate phase modulator. Future data acquisition improvements are suggested that will bring the phase sensitivity exactly to the standard quantum limit, and beyond the quantum limit by squeezing.
This study addresses any sensor based on measuring a physical quantity through the phase of a probing beam. This includes sensing of rotation, acceleration, index change, displacement, fields… While most phase measurements are made by detecting an amplitude change in interfering beams, we detect instead a phase change through a relative frequency shift of two correlated frequency combs. This paper explores the limit sensitivity that this method can achieve, when the combs are generated in an Optical Parametric Oscillator (OPO), pumped synchronously by a train of femtosecond pulses separated by half the OPO cavity round-trip time. It is shown that a phase difference as small as 0.4 nanoradians can be resolved between the two pulses circulating in the cavity. This phase difference is one order of magnitude better than the previous record. The root-mean-square deviation of the measured phase over measuring time is close to the standard quantum limit (phase-photon number uncertainty product of 0.66). Innovations that made such improved performances possible include a more stable OPO cavity design; a stabilization system with a novel purely electronic locking of the OPO cavity length relative to that of the pump laser; a shorter pump laser cavity; and a square pulse generator for driving a 0.5 mm pathlength lithium niobate phase modulator. Future data acquisition improvements are suggested that will bring the phase sensitivity exactly to the standard quantum limit, and beyond the quantum limit by squeezing.
When a linear Optical Parametric Oscillator (OPO) is pumped at twice the round-trip rate of its cavity, it generates an optical comb. This comb is degenerate, made by two intertwined undistinguishable pulse trains at half the repletion rate of the pump. If one pulse experiences a phase shift at each round-trip, the degeneracy is lifted, and each tooth of the comb splits in two. Even though each comb of this unstabilized source has a bandwidth of tens of MHz, interfering them on a detector leads to a beat note with a bandwidth vanishing the closer to degeneracy. At 3 Hz beat note, we measure a bandwidth of 0.003 Hz (FWHM of the beat note spectrum), corresponding to a phase resolution of 50 picoradian, or an optical path difference of 10 attometer. Several applications will be discussed, ranging from inertial navigation to magnetometry to gravitational wave detection.
We show that synchronously pumped Optical Parametric Oscillators are able to generate strongly squeezed trains of femtosecond pulses in “supermodes”, which are well defined superpositions of many modes of different frequencies. In some conditions, several supermodes can be simultaneously squeezed. In addition, we show that the use of such squeezed trains of pulses can improve time transfer between remote clocks and ranging techniques beyond the standard quantum limit provided they have an optimized temporal shape.
Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables [1]. They can be generated either by mixing different squeezed light sources using linear optical operations [2], or directly in a multimode optical device [3, 4]. Synchronously Pumped Optical Parametric Oscillators (SPOPO) — which correspond to an OPO pumped by a train of ultrashort pulses that are synchronized with the cavity round-trip time — have been theoretically shown to be promising devices for the generation of multimode nonclassical frequency combs, since a SPOPO is a sole optical cavity acting as an assembly of independent squeezers in a particular basis called the supermodes basis [5]. The supermodes are optical frequency combs with specific spectrum and phase profiles that are determined by the length of the intracavity nonlinear crystal and the pulse shape of the pump.
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.
The quantum statistics of a laser result in noise when measurements of the beam are made. This noise sets a classical limit beyond which a laser cannot be used with increasing sensitivity. This quantum noise limit is imposed on many of the uses of lasers currently, especially in power limited devices such as optical communications. The statistics of the laser photon field can be modified to produce a non-classical state resulting in lower noise than the quantum noise limit when detected appropriately. This state, called a squeezed state, has been measured previously from a cavity enhanced optical parametric oscillator (OPO) only at frequency sidebands within the linewidth of the cavity. ¶ This thesis reports measurements of squeezing at microwave frequency sidebands on an optical beam produced by an optical parametric oscillator. This is the first reported measurement of squeezing at frequency sidebands at higher longitudinal modes of the cavity from an OPO. Noise reduction below the quantum noise limit is measured at sideband frequencies of 5 MHz, 1.7 GHz, 3.4 GHz and 5.1 GHz, corresponding to the zeroth, first, second and third longitudinal modes from the squeezed beam. These results are the highest frequency sideband measurements of squeezing to date. In addition to measuring squeezing at different longitudinal modes for the fundamental Gaussian spatial mode, non-classical noise reduction is measured at the same frequencies for a squeezed higher order spatial mode, TEM10. ¶ A single mode theoretical model of the OPO is presented, based on the work of ref. [1]. Computer simulations of the squeezing predicted by this model are developed and compared to the experimental results, showing excellent agreement between the different longitudinal modes for each of the two spatial modes measured.
Multimode squeezed light is a key resource for quantum technologies, enabling applications in boson sampling, quantum networks, and optical quantum computation [1],[2]. Parametric down-conversion in synchronously pumped optical parametric oscillators (SPOPOs) offers a versatile platform for generating multimode squeezed states across the time-frequency domain. In these systems, supermodes manifest as independent quantum states in the temporal domain and as frequency combs in the spectral domain [3]. Precise control of these states is crucial for quantum applications and requires an experimental setup capable of fine-tuning multiple parameters to optimize squeezing properties. In this work, we present an experimental setup for generating and characterizing multimode vacuum squeezed states using a SPOPO and a balanced homodyne detection scheme. Two spatial light modulators (SLMs) placed on the pump and local oscillator (LO) beams provide full control over their spectral properties, including amplitude and phase shaping. This flexibility allows us to optimize the experimental conditions and investigate squeezing dependence on key parameters such as the LO spectral detuning and bandwidth. By introducing a programmableπ-phase shift to the LO via the SLM, we selectively probe the multimode structure, distinguishing between even and odd supermodes. Additionally, the SLM on the pump can introduce an arbitrary chirp, further enhancing control over the system. Our setup, schematized in Figure 1a, is based on a commercial mode-locked Yb-fiber laser operating at 93MHz, emitting pulses centered at 1035nm with a 10nm bandwidth. A portion of the radiation is frequency-doubled to 517.5nm via an LBO crystal to serve as the pump for the SPOPO, while the remaining part is used as the LO for homodyne detection after transmission through the SPOPO cavity, ensuring high beam quality. The SPOPO cavity is frequency-locked to the laser via a Pound-Drever-Hall technique, ensuring stable and optimized operation. Figure 1b presents representative measurements of squeezing levels as a function of the LO spectral bandwidth, showing how its symmetric or antisymmetric phase influences the detection of different supermodes and, consequently, the squeezing level depending on their structure. The measurements were performed using lithium niobate (LNB) nonlinear crystals of 3.0mm and 1.5mm lengths. Our setup allows for future investigations of dispersion effects on squeezing, thus far only theoretically predicted [4], by introducing chirped mirrors for dispersion compensation. Moreover, different nonlinear crystals, such as lithium niobate, beta barium borate (BBO), and lithium triborate (LBO) of various lengths, will be tested to explore the multimode properties of the squeezed states. These investigations will provide insights into the experimental conditions required to achieve single-mode squeezing, crucial for applications such as Gaussian Boson Sampling, with results to be presented at the conference.