arXiv subjects

Roman Schnabel

Publications and source records attributed to Roman Schnabel.

At least 127 records · Page 7Linked to original sources

arXiv2009

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation.

quant-ph↗

arXiv2009

Markov Chain Monte Carlo Estimation of Quantum States

We apply a Bayesian data analysis scheme known as the Markov Chain Monte Carlo (MCMC) to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical information concerning all reconstruction parameters including their statistical correlations with no a priori assumptions as to the form of the distribution from which it has been obtained. From this vector can be derived, e. g. the marginal distributions and uncertainties of all model parameters and also of other quantities such as the purity of the reconstructed state. We demonstrate the utility of this scheme by reconstructing the Wigner function of phase-diffused squeezed states. These states posses non-Gaussian statistics and therefore represent a non-trivial case of tomographic reconstruction. We compare our results to those obtained through pure maximum-likelihood and Fisher information approaches.

quant-ph↗

arXiv2009

Observation of continuous-wave squeezed light at 1550 nm

We report on the generation of continuous-wave squeezed vacuum states of light at the telecommunication wavelength of 1550 nm. The squeezed vacuum states were produced by type I optical parametric amplification (OPA) in a standing-wave cavity built around a periodically poled potassium titanyl phosphate (PPKTP) crystal. A non-classical noise reduction of 5.3 dB below the shot noise was observed by means of balanced homodyne detection.

quant-ph↗

arXiv2008

Preparation of distilled and purified continuous variable entangled states

The distribution of entangled states of light over long distances is a major challenge in the field of quantum information. Optical losses, phase diffusion and mixing with thermal states lead to decoherence and destroy the non-classical states after some finite transmission-line length. Quantum repeater protocols, which combine quantum memory, entanglement distillation and entanglement swapping, were proposed to overcome this problem. Here we report on the experimental demonstration of entanglement distillation in the continuous-variable regime. Entangled states were first disturbed by random phase fluctuations and then distilled and purified using interference on beam splitters and homodyne detection. Measurements of covariance matrices clearly indicate a regained strength of entanglement and purity of the distilled states. In contrast to previous demonstrations of entanglement distillation in the complementary discrete-variable regime, our scheme achieved the actual preparation of the distilled states, which might therefore be used to improve the quality of downstream applications such as quantum teleportation.

quant-ph↗

arXiv2008

Creation of a quantum oscillator by classical control

As a pure quantum state is being approached via linear feedback, and the occupation number approaches and eventually goes below unity, optimal control becomes crucial. We obtain theoretically the optimal feedback controller that minimizes the uncertainty for a general linear measurement process, and show that even in the absence of classical noise, a pure quantum state is not always achievable via feedback. For Markovian measurements, the deviation from minimum Heisenberg Uncertainty is found to be closely related to the extent to which the device beats the free-mass Standard Quantum Limit for force measurement. We then specialize to optical Markovian measurements, and demonstrate that a slight modification to the usual input-output scheme -- either injecting frequency independent squeezed vacuum or making a homodyne detection at a non-phase quadrature -- allows controlled states of kilogram-scale mirrors in future LIGO interferometers to reach occupation numbers significantly below unity.

quant-ph↗

arXiv2008

Double optical spring enhancement for gravitational wave detectors

Currently planned second-generation gravitational-wave laser interferometers such as Advanced LIGO exploit the extensively investigated signal-recycling (SR) technique. Candidate Advanced LIGO configurations are usually designed to have two resonances within the detection band, around which the sensitivity is enhanced: a stable optical resonance and an unstable optomechanical resonance - which is upshifted from the pendulum frequency due to the so-called optical-spring effect. Alternative to a feedback control system, we propose an all-optical stabilization scheme, in which a second optical spring is employed, and the test mass is trapped by a stable ponderomotive potential well induced by two carrier light fields whose detunings have opposite signs. The double optical spring also brings additional flexibility in re-shaping the noise spectral density and optimizing toward specific gravitational-wave sources. The presented scheme can be extended easily to a multi-optical-spring system that allows further optimization.

gr-qc↗

arXiv2008

Observation of entanglement between two light beams spanning an octave in optical frequency

We have experimentally demonstrated how two beams of light separated by an octave in frequency can become entangled after their interaction in a second-order nonlinear medium. The entangler consisted of a nonlinear crystal placed within an optical resonator that was strongly driven by coherent light at the fundamental and second-harmonic wavelengths. An inter-conversion between the fields created quantum correlations in the amplitude and phase quadratures, which were measured by two independent homodyne detectors. Analysis of the resulting correlation matrix revealed a wavefunction inseparability of 0.74(1) < 1 thereby satisfying the criterion of entanglement.

quant-ph↗

arXiv2007

Multiple copy distillation and purification of phase diffused squeezed states

We provide a detailed theoretical analysis of multiple copy purification and distillation protocols for phase diffused squeezed states of light. The standard iterative distillation protocol is generalized to a collective purification of an arbitrary number of N copies. We also derive a semi-analytical expression for the asymptotic limit of the iterative distillation and purification protocol and discuss its properties.

quant-ph↗

arXiv2007

Entanglement of macroscopic test masses and the Standard Quantum Limit in laser interferometry

We show that the generation of entanglement of two heavily macroscopic mirrors with masses of up to several kilograms are feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the Standard Quantum Limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and provides a measure of when macroscopic entanglement can be observed in the presence of realistic decoherence processes.

quant-ph↗

arXiv2007

On the mechanical quality factors of cryogenic test masses from fused silica and crystalline quartz

Current interferometric gravitational wave detectors (IGWDs) are operated at room temperature with test masses made from fused silica. Fused silica shows very low absorption at the laser wavelength of 1064 nm. It is also well suited to realize low thermal noise floors in the detector signal band since it offers low mechanical loss, i. e. high quality factors (Q factors) at room temperature. However, for a further reduction of thermal noise, cooling the test masses to cryogenic temperatures may prove an interesting technique. Here we compare the results of Q factor measurements at cryogenic temperatures of acoustic eigenmodes of test masses from fused silica and its crystalline counterpart. Our results show that the mechanical loss of fused silica increases with lower temperature and reaches a maximum at 30 K for frequencies of slightly above 10 kHz. The losses of crystalline quartz generally show lower values and even fall below the room temperature values of fused silica below 10 K. Our results show that in comparison to fused silica, crystalline quartz has a considerably narrower and lower dissipation peak on cooling and thus has more promise as a test mass material for IGDWs operated at cryogenic temperatures. The origin of the different Q factor versus temperature behavior of the two materials is discussed.

gr-qc↗

arXiv2007

Local readout enhancement for detuned signal-recycling interferometers

Motivated by the optical-bar scheme of Braginsky, Gorodetsky and Khalili, we propose to add to a high power detuned signal-recycling interferometer a local readout scheme which measures the motion of the arm-cavity front mirror. At low frequencies this mirror moves together with the arm-cavity end mirror, under the influence of gravitational waves. This scheme improves the low-frequency quantum-noise-limited sensitivity of optical-spring interferometers significantly and can be considered as a incorporation of the optical-bar scheme into currently planned second-generation interferometers. On the other hand it can be regarded as an extension of the optical bar scheme. Taking compact-binary inspiral signals as an example, we illustrate how this scheme can be used to improve the sensitivity of the planned Advanced LIGO interferometer, in various scenarios, using a realistic classical-noise budget. We also discuss how this scheme can be implemented in Advanced LIGO with relative ease.

gr-qc↗

arXiv2007

Quantum engineering of squeezed states for quantum communication and metrology

We report the experimental realization of squeezed quantum states of light, tailored for new applications in quantum communication and metrology. Squeezed states in a broad Fourier frequency band down to 1 Hz has been observed for the first time. Nonclassical properties of light in such a low frequency band is required for high efficiency quantum information storage in electromagnetically induced transparency (EIT) media. The states observed also cover the frequency band of ultra-high precision laser interferometers for gravitational wave detection and can be used to reach the regime of quantum non-demolition interferometry. And furthermore, they cover the frequencies of motions of heavily macroscopic objects and might therefore support the attempts to observe entanglement in our macroscopic world.

quant-ph↗

arXiv2007

Detuned Twin-Signal-Recycling for ultra-high precision interferometers

We propose a new interferometer technique for high precision phase measurements such as those in gravitational wave detection. The technique utilizes a pair of optically coupled resonators that provides identical resonance conditions for the upper as well the lower phase modulation signal sidebands. This symmetry significantly reduces the noise spectral density in a wide frequency band compared with single sideband recycling topologies of current and planned gravitational wave detectors. Furthermore the application of squeezed states of light becomes less demanding.

quant-ph↗

arXiv2007

Squeezed-field injection for gravitational wave interferometers

In a recent table-top experiment we demonstrated the compatibility of three advanced interferometer techniques for gravitational wave detection, namely power-recycling, detuned signal-recycling and squeezed field injection. The interferometer's signal to noise ratio was improved by up to 2.8 dB beyond the coherent state's shot-noise. This value was mainly limited by optical losses on the squeezed field. We present a detailed analysis of the optical losses of in our experiment and provide an estimation of the possible nonclassical performance of a future squeezed field enhanced GEO600 detector.

quant-ph↗

arXiv2007

Demonstration of a squeezed light enhanced power- and signal-recycled Michelson interferometer

We report on the experimental combination of three advanced interferometer techniques for gravitational wave detection, namely power-recycling, detuned signal-recycling and squeezed field injection. For the first time we experimentally prove the compatibility of especially the latter two. To achieve a broadband non-classical sensitivity improvement we applied a filter cavity for compensation of quadrature rotation. Signal to noise ratio was improved by up to 2.8 dB beyond the coherent state's shot noise. The complete set-up was stably locked for arbitrary times and characterized by injected single-sideband modulation fields.

quant-ph↗

arXiv2007

Coherent control of vacuum squeezing in the Gravitational-Wave Detection Band

We propose and demonstrate a coherent control scheme for stable phase locking of squeezed vacuum fields. We focus on sideband fields at frequencies from 10Hz to 10kHz which is a frequency regime of particular interest in gravitational wave detection and for which conventional control schemes have failed so far. A vacuum field with broadband squeezing covering this entire band was produced using optical parametric oscillation and characterized with balanced homodyne detection. The system was stably controlled over long periods utilizing two coherent but frequency shifted control fields. In order to demonstrate the performance of our setup the squeezed field was used for a nonclassical sensitivity improvement of a Michelson interferometer at audio frequencies.

quant-ph↗

arXiv2007

Experimental characterization of frequency dependent squeezed light

We report on the demonstration of broadband squeezed laser beams that show a frequency dependent orientation of the squeezing ellipse. Carrier frequency as well as quadrature angle were stably locked to a reference laser beam at 1064nm. This frequency dependent squeezing was characterized in terms of noise power spectra and contour plots of Wigner functions. The later were measured by quantum state tomography. Our tomograph allowed a stable lock to a local oscillator beam for arbitrary quadrature angles with one degree precision. Frequency dependent orientations of the squeezing ellipse are necessary for squeezed states of light to provide a broadband sensitivity improvement in third generation gravitational wave interferometers. We consider the application of our system to long baseline interferometers such as a future squeezed light upgraded GEO600 detector.

quant-ph↗

arXiv2007

Experimental characterization of Gaussian quantum communication channels

We present a full experimental characterization of continuous variable quantum communication channels established by shared entanglement together with local operations and classical communication. The resulting teleportation channel was fully characterized by measuring all elements of the covariance matrix of the shared two-mode squeezed Gaussian state. From the experimental data we determined the lower bound to the quantum channel capacity, the teleportation fidelity of coherent states and the logarithmic negativity and the purity of the shared state. Additionally, a positive secret key rate was obtained for two of the established channels.

quant-ph↗