arXiv subjects

R. Schnabel

Publications and source records attributed to R. Schnabel.

At least 19 recordsLinked to original sources

arXiv2020

Quantum correlations between the light and kilogram-mass mirrors of LIGO

Measurement of minuscule forces and displacements with ever greater precision encounters a limit imposed by a pillar of quantum mechanics: the Heisenberg uncertainty principle. A limit to the precision with which the position of an object can be measured continuously is known as the standard quantum limit (SQL). When light is used as the probe, the SQL arises from the balance between the uncertainties of photon radiation pressure imposed on the object and of the photon number in the photoelectric detection. The only possibility surpassing the SQL is via correlations within the position/momentum uncertainty of the object and the photon number/phase uncertainty of the light it reflects. Here, we experimentally prove the theoretical prediction that this type of quantum correlation is naturally produced in the Laser Interferometer Gravitational-wave Observatory (LIGO). Our measurements show that the quantum mechanical uncertainties in the phases of the 200 kW laser beams and in the positions of the 40 kg mirrors of the Advanced LIGO detectors yield a joint quantum uncertainty a factor of 1.4 (3dB) below the SQL. We anticipate that quantum correlations will not only improve gravitational wave (GW) observatories but all types of measurements in future.

quant-ph↗

arXiv2016

GEO 600 and the GEO-HF upgrade program: successes and challenges

The German-British laser-interferometric gravitational wave detector GEO 600 is in its 14th year of operation since its first lock in 2001. After GEO 600 participated in science runs with other first-generation detectors, a program known as GEO-HF began in 2009. The goal was to improve the detector sensitivity at high frequencies, around 1 kHz and above, with technologically advanced yet minimally invasive upgrades. Simultaneously, the detector would record science quality data in between commissioning activities. As of early 2014, all of the planned upgrades have been carried out and sensitivity improvements of up to a factor of four at the high-frequency end of the observation band have been achieved. Besides science data collection, an experimental program is ongoing with the goal to further improve the sensitivity and evaluate future detector technologies. We summarize the results of the GEO-HF program to date and discuss its successes and challenges.

physics.ins-det↗

arXiv2013

Impact of backscattered light in a squeezing-enhanced interferometric gravitational-wave detector

Squeezed states of light have been recently used to improve the sensitivity of laser interferometric gravitational-wave detectors beyond the quantum limit. To completely establish quantum engineering as a realistic option for the next generation of detectors, it is crucial to study and quantify the noise coupling mechanisms which injection of squeezed states could potentially introduce. We present a direct measurement of the impact of backscattered light from a squeezed-light source deployed on one of the 4 km long detectors of the Laser Interferometric Gravitational Wave Observatory (LIGO). We also show how our measurements inform the design of squeezed light sources compatible with the even more sensitive advanced detectors currently under construction, such as Advanced LIGO.

quant-ph↗

arXiv2013

First Long-Term Application of Squeezed States of Light in a Gravitational-Wave Observatory

We report on the first long-term application of squeezed vacuum states of light to improve the shot-noise-limited sensitivity of a gravitational-wave observatory. In particular, squeezed vacuum was applied to the German/British detector GEO600 during a period of three months from June to August 2011, when GEO600 was performing an observational run together with the French/Italian Virgo detector. In a second period squeezing application continued for about 11 months from November 2011 to October 2012. During this time, squeezed vacuum was applied for 90.2% (205.2 days total) of the time that science-quality data was acquired with GEO600. Sensitivity increase from squeezed vacuum application was observed broad-band above 400Hz. The time average of gain in sensitivity was 26% (2.0dB), determined in the frequency band from 3.7kHz to 4.0kHz. This corresponds to a factor of two increase in observed volume of the universe, for sources in the kHz region (e.g. supernovae, magnetars). We introduce three new techniques to enable stable long-term application of squeezed light, and show that the glitch-rate of the detector did not increase from squeezing application. Squeezed vacuum states of light have arrived as a permanent application, capable of increasing the astrophysical reach of gravitational-wave detectors.

physics.ins-det↗

arXiv2012

Balanced Homodyne Detection of Optical Quantum States at Audio-Band Frequencies and Below

The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of the relevant noise sources and the methods by which they can be identified and mitigated in order to achieve quantum noise limited balanced homodyne detection. Using these techniques, flat shot-noise down to Fourier frequencies below 0.5 Hz is produced. This enables the direct observation of large magnitudes of squeezing across the entire audio-band, of particular interest for ground-based interferometric gravitational wave detectors. 11.6 dB of shot-noise suppression is directly observed, with more than 10 dB down to 10 Hz.

quant-ph↗

arXiv2012

Preparing the bound instance of quantum entanglement

Among the possibly most intriguing aspects of quantum entanglement is that it comes in "free" and "bound" instances. Bound entangled states require entangled states in preparation but, once realized, no free entanglement and therefore no pure maximally entangled pairs can be regained. Their existence hence certifies an intrinsic irreversibility of entanglement in nature and suggests a connection with thermodynamics. In this work, we present a first experimental unconditional preparation and detection of a bound entangled state of light. We consider continuous-variable entanglement, use convex optimization to identify regimes rendering its bound character well certifiable, and realize an experiment that continuously produced a distributed bound entangled state with an extraordinary and unprecedented significance of more than ten standard deviations away from both separability and distillability. Our results show that the approach chosen allows for the efficient and precise preparation of multimode entangled states of light with various applications in quantum information, quantum state engineering and high precision metrology.

quant-ph↗

arXiv2011

Direct Sampling of Negative Quasiprobabilities of a Squeezed State

Although squeezed states are nonclassical states, so far, their nonclassicality could not be demonstrated by negative quasiprobabilities. In this work we derive pattern functions for the direct experimental determination of so-called nonclassicality quasiprobabilities. The negativities of these quantities turn out to be necessary and sufficient for the nonclassicality of an arbitrary quantum state and are therefore suitable for a direct and general test of nonclassicality. We apply the method to a squeezed vacuum state of light that was generated by parametric down-conversion in a second-order nonlinear crystal.

quant-ph↗

arXiv2011

Entangled Qubits in a non-Gaussian Quantum State

We experimentally generate and tomographically characterize a mixed, genuinely non-Gaussian bipartite continuous-variable entangled state. By testing entanglement in 2$\times$2-dimensional two-qubit subspaces, entangled qubits are localized within the density matrix, which, firstly, proves the distillability of the state and, secondly, is useful to estimate the efficiency and test the applicability of distillation protocols. In our example, the entangled qubits are arranged in the density matrix in an asymmetric way, i.e. entanglement is found between diverse qubits composed of different photon number states, although the entangled state is symmetric under exchanging the modes.

quant-ph↗

arXiv2011

Laser interferometry with translucent and absorbing mechanical oscillators

The sensitivity of laser interferometers can be pushed into regimes that enable the direct observation of quantum behaviour of mechanical oscillators. In the past, membranes with subwavelength thickness (thin films) have been proposed as high-mechanical-quality, low-thermal-noise oscillators. Thin films from a homogenous material, however, generally show considerable light transmission accompanied by heating due to light absorption, which typically reduces the mechanical quality and limits quantum opto-mechanical experiments in particular at low temperatures. In this work, we experimentally analyze a Michelson-Sagnac interferometer including a translucent silicon nitride (SiN) membrane with subwavelength thickness. We find that such an interferometer provides an operational point being optimally suited for quantum opto-mechanical experiments with translucent oscillators. In case of a balanced beam splitter of the interferometer, the membrane can be placed at a node of the electro-magnetic field, which simultaneously provides lowest absorption and optimum laser noise rejection at the signal port. We compare the optical and mechanical model of our interferometer with experimental data and confirm that the SiN membrane can be coupled to a laser power of the order of one Watt at 1064 nm without significantly degrading the membrane's quality factor of the order 10^6, at room temperature.

physics.optics↗

arXiv2009

Building blocks for future detectors: Silicon test masses and 1550 nm laser light

Current interferometric gravitational wave detectors use the combination of quasi-monochromatic, continuous-wave laser light at 1064 nm and fused silica test masses at room temperature. Detectors of the third generation, such as the Einstein-Telescope, will involve a considerable sensitivity increase. The combination of 1550 nm laser radiation and crystalline silicon test masses at low temperatures might be important ingredients in order to achieve the sensitivity goal. Here we compare some properties of the fused silica and silicon test mass materials relevant for decreasing the thermal noise in future detectors as well as the recent technology achievements in the preparation of laser radiation at 1064 nm and 1550 nm relevant for decreasing the quantum noise. We conclude that silicon test masses and 1550 nm laser light have the potential to form the future building blocks of gravitational wave detection.

physics.ins-det↗

arXiv2009

Coupling of lateral grating displacement to the output ports of a diffractive Fabry-Perot cavity

Diffraction gratings have been proposed as core elements in future laser-interferometric gravitational-wave detectors. In this paper, we use a steady-state technique to derive coupling of lateral grating displacement to the output ports of a diffractive Fabry-Perot cavity. By introducing a signal to noise ratio (SNR) for each of the three cavity output ports the magnitude of the noise sidebands originating from lateral grating displacement are compared to the magnitude of a potential gravitational wave signal. For the example of a 3km long Fabry-Perot cavity featuring parameters similar to the planned Advanced Virgo instrument, we found that the forward-reflecting grating port offers the highest SNR at low frequencies. Furthermore, for this example suspension requirements for lateral isolation were computed, and a factor of twenty relaxation at a frequency of 10Hz can be gained over the transmitted port by observing the forward-reflected port.

gr-qc↗

arXiv2008

Experimental test of nonclassicality criteria

We experimentally examine the nonclassical character of a class of non-Gaussian states known as phase-diffused squeezed states. These states may show no squeezing effect at all, and therefore provide an interesting example to test nonclassicality criteria. The characteristic function of the Glauber-Sudarshan representation (P function) proves to be a powerful tool to detect nonclassicality. Using this criterion we find that phase-diffused squeezed states are always nonclassical, even if the squeezing effect vanishes. Testing other criteria of nonclassicality based on higher-order squeezing and the positive semidefinitness of special matrices of normally ordered moments, it is found that these criteria fail to reveal the nonclassicality for some of the prepared phase-diffused squeezed states.

quant-ph↗

arXiv2007

Phase and alignment noise in grating interferometers

Diffraction gratings have been proposed as core optical elements in future laser-interferometric gravitational-wave detectors. In this paper we derive equations for the coupling between alignment noise and phase noise at diffraction gratings. In comparison to a standard reflective component (mirror or beam splitter) the diffractive nature of the gratings causes an additional coupling of geometry changes into alignment and phase noise. Expressions for the change in angle and optical path length of each outgoing beam are provided as functions of a translation or rotation of the incoming beam with respect to the grating. The analysis is based entirely on the grating equation and the geometry of the setup. We further analyse exemplary optical setups which have been proposed for the use in future gravitational wave detectors. We find that the use of diffraction gratings yields a strong coupling of alignment noise into phase noise. By comparing the results with the specifications of current detectors we show that this additional noise coupling results in new, challenging requirements for the suspension and isolation systems for the optical components.

gr-qc↗

arXiv2007

On the distillation and purification of phase-diffused squeezed states

Recently it was discovered that non-Gaussian decoherence processes, such as phase-diffusion, can be counteracted by purification and distillation protocols that are solely built on Gaussian operations. Here, we make use of this experimentally highly accessible regime, and provide a detailed experimental and theoretical analysis of several strategies for purification/distillation protocols on phase-diffused squeezed states. Our results provide valuable information for the optimization of such protocols with respect to the choice of the trigger quadrature, the trigger threshold value and the probability of generating a distilled state.

quant-ph↗

arXiv2007

Optical characterization of ultra-high diffraction efficiency gratings

We report on the optical characterization of an ultra-high diffraction efficiency grating in 1st order Littrow configuration. The apparatus used was an optical cavity built from the grating under investigation and an additional high reflection mirror. Measurement of the cavity finesse provided precise information about the grating's diffraction efficiency and its optical loss. We measured a finesse of 1580 from which we deduced a diffraction efficiency of (99.635$\pm$0.016)% and an overall optical loss due to scattering and absorption of just 0.185 %. Such high quality gratings, including the tool used for their characterization, might apply for future gravitational wave detectors. For example the demonstrated cavity itself presents an all-reflective, low-loss Fabry-Perot resonator that might replace conventional arm cavities in advanced high power Michelson interferometers.

physics.optics↗

arXiv2007

Diffractive Optics for Gravitational Wave Detectors

All-reflective interferometry based on nano-structured diffraction gratings offers new possibilities for gravitational wave detection. We investigate an all-reflective Fabry-Perot interferometer concept in 2nd order Littrow mount. The input-output relations for such a resonator are derived treating the grating coupler by means of a scattering matrix formalism. A low loss dielectric reflection grating has been designed and manufactured to test the properties of such a grating cavity.

physics.optics↗

arXiv2007

Low-loss grating for coupling to a high-finesse cavity

A concept for a low loss all-reflective cavity coupler is experimentally demonstrated at a wavelength of 1064 nm. A 1450 nm period dielectric reflection grating with a diffraction efficiency of 0.58 % in the -1st order is used in 2nd order Littrow configuration as a coupler to form a cavity with a finesse of 400. The application of such reflective low-loss cavity couplers in future generations of gravitational-wave detectors as well as some implementation issues are discussed.

physics.optics↗

arXiv2007

Input-output relations for a 3-port grating coupled Fabry-Perot cavity

We analyze an optical 3-port reflection grating by means of a scattering matrix formalism. Amplitude and phase relations between the 3 ports, i.e. the 3 orders of diffraction are derived. Such a grating can be used as an all-reflective, low-loss coupler to Fabry-Perot cavities. We derive the input output relations of a 3-port grating coupled cavity and find distinct properties not present in 2-port coupled cavities. The cavity relations further reveal that the 3-port coupler can be designed such that the additional cavity port interferes destructively. In this case the all-reflective, low-loss, single-ended Fabry-Perot cavity becomes equivalent to a standard transmissive, 2-port coupled cavity.

physics.optics↗