scholarly journals A Broadband Signal Recycling Scheme for Approaching the Quantum Limit from Optical Losses

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 3
Author(s):  
Teng Zhang ◽  
Joe Bentley ◽  
Haixing Miao
Keyword(s):  
Lower Bound ◽  
Thermal Noise ◽  
Quantum Noise ◽  
Quantum Limit ◽  
Optical Losses ◽  
Signal Amplifier ◽  
Broadband Signal ◽  
The Difference ◽  
White Light Cavity ◽  
Laser Interferometric

Quantum noise limits the sensitivity of laser interferometric gravitational-wave detectors. Given the state-of-the-art optics, the optical losses define the lower bound of the best possible quantum-limited detector sensitivity. In this work, we come up with a broadband signal recycling scheme which gives a potential solution to approaching this lower bound by converting the signal recycling cavity to be a broadband signal amplifier using an active optomechanical filter. We will show the difference and advantage of such a scheme compared with the previous white light cavity scheme using the optomechanical filter in [Phys.Rev.Lett.115.211104 (2015)]. The drawback is that the new scheme is more susceptible to the thermal noise of the mechanical oscillator.

scholarly journals A broadband signal recycling scheme for saturating the quantum limit from optical losses

2020 ◽  
Author(s):  
Teng Zhang ◽  
Joe Bentley ◽  
Haixing Miao
Keyword(s):  
Lower Bound ◽  
Quantum Noise ◽  
Quantum Limit ◽  
Optical Losses ◽  
Signal Amplifier ◽  
Broadband Signal ◽  
The Difference ◽  
Output Filter ◽  
White Light Cavity ◽  
Laser Interferometric

Quantum noise limits the sensitivity of laser interferometric gravitational-wave detectors. Given the state-of-the-art optics, the optical losses define the lower bound of best possible quantum-limited detector sensitivity. In this work, we come up with the configuration which allows to saturate this lower bound by converting the signal recycling cavity to be a broadband signal amplifier using an active optomechanical filter. We will show the difference and advantage of such a broadband signal recycling scheme compared with the previous white-light-cavity scheme using the optomechanical filter in [Phys.Rev.Lett.115.211104 (2015)]. The drawback is that the new scheme is more susceptible to the thermal noise of the mechanical oscillator. To suppress the radiation pressure noise which rises along with the signal amplification, squeezing with input/output filter cavities and heavier test mass are used in this work.

INTERACTION OF MESOSCOPIC JOSEPHSON JUNCTION WITH A SUCCESSIVE SQUEEZED COHERENT FIELD

2000 ◽  
Vol 14 (16) ◽  
pp. 609-618
Author(s):  
V. A. POPESCU
Keyword(s):  
Coherent State ◽  
Josephson Junction ◽  
Coherent States ◽  
Quantum Noise ◽  
Shapiro Steps ◽  
Superconducting Ring ◽  
Coherent Field ◽  
Current Voltage ◽  
Quantum Current ◽  
The Difference

Signal-to-quantum noise ratio for quantum current in mesoscopic Josephson junction of a circular superconducting ring can be improved if the electromagnetic field is in a successive squeezed coherent state. The mesoscopic Josephson junctions can feel the difference between the successive squeezed coherent states and other types of squeezed coherent states because their current–voltage Shapiro steps are different. We compare our method with another procedure for superposition of two squeezed coherent states (a squeezed even coherent state) and consider the effect of different large inductances on the supercurrent.

scholarly journals An improved lower bound related to the Furstenberg-Sárközy theorem

10.37236/4656 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Mark Lewko
Keyword(s):  
Lower Bound ◽  
The Other ◽  
The Difference

Let $D(n)$ denote the cardinality of the largest subset of the set $\{1,2,\ldots,n\}$ such that the difference of no pair of distinct elements is a square. A well-known theorem of Furstenberg and Sárközy states that $D(n)=o(n)$. In the other direction, Ruzsa has proven that $D(n) \gtrsim n^{\gamma}$ for $\gamma = \frac{1}{2}\left( 1 + \frac{\log 7}{\log 65} \right) \approx 0.733077$. We improve this to $\gamma = \frac{1}{2}\left( 1 + \frac{\log 12}{\log 205} \right)  \approx 0.733412$.

scholarly journals A lower bound for a remainder term associated with the sum of digits function

1991 ◽  
Vol 34 (1) ◽  
pp. 121-142 ◽  
Author(s):  
D. M. E. Foster
Keyword(s):  
Lower Bound ◽  
Positive Integer ◽  
Upper Bound ◽  
Remainder Term ◽  
Fixed Integer ◽  
Sum Of Digits ◽  
Sum Of Digits Function ◽  
The Difference

For a fixed integer q≧2, every positive integer k = Σr≧0ar(q, k)qr where each ar(q, k)∈{0,1,2,…, q−1}. The sum of digits function α(q, k) Σr≧0ar(q, k) behaves rather erratically but on averaging has a uniform behaviour. In particular if , where n>1, then it is well known that A(q, n)∼½((q − 1)/log q)n logn as n → ∞. For odd values of q, a lower bound is now obtained for the difference 2S(q, n) = A(q, n)−½(q − 1))[log n/log q, where [log n/log q] denotes the greatest integer ≦log n /log q. This complements an upper bound already found.

scholarly journals Measurement of quantum noise in a single-electron transistor near the quantum limit

2009 ◽  
Vol 5 (9) ◽  
pp. 660-664 ◽  
Author(s):  
W. W. Xue ◽  
Z. Ji ◽  
Feng Pan ◽  
Joel Stettenheim ◽  
M. P. Blencowe ◽  
...  
Keyword(s):  
Quantum Noise ◽  
Single Electron ◽  
Quantum Limit ◽  
Single Electron Transistor

scholarly journals COMPLEMENTARITY IN GENERIC OPEN QUANTUM SYSTEMS

2010 ◽  
Vol 24 (24) ◽  
pp. 2485-2509 ◽  
Author(s):  
SUBHASHISH BANERJEE ◽  
R. SRIKANTH
Keyword(s):  
Lower Bound ◽  
Uniform Distribution ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Atomic Systems ◽  
Information Theoretic ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
The Difference ◽  
Positive Operator Valued Measure

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian observable and phase as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as a lower bound on entropy excess, X, the difference between the entropy of one variable, typically the number, and the knowledge of its complementary variable, typically the phase, where knowledge of a variable is defined as its relative entropy with respect to the uniform distribution. In the case of finite-dimensional systems, a weighting of phase knowledge by a factor μ (> 1) is necessary in order to make the bound tight, essentially on account of the POVM nature of phase as defined here. Numerical and analytical evidence suggests that μ tends to 1 as the system dimension becomes infinite. We study the effect of non-dissipative and dissipative noise on these complementary variables for an oscillator as well as atomic systems.

MODE COMPETITION IN A TWO-MODE LASER SYSTEM SUBJECT TO BOTH PUMP NOISE AND QUANTUM NOISE

2009 ◽  
Vol 23 (20n21) ◽  
pp. 2483-2495
Author(s):  
YOULIN XIANG ◽  
DONGCHENG MEI
Keyword(s):  
Quantum Noise ◽  
Laser Intensity ◽  
Phase Locking ◽  
Laser System ◽  
Mode Competition ◽  
Langevin Equations ◽  
Line Center ◽  
Coupling Constant ◽  
Absolute Value ◽  
The Difference

The laser intensity Langevin equations for a two-mode ring laser subject to both pump noise and quantum noise have been obtained by a phase-locking method. By means of stochastic simulation, the mode competition between two modes for different combinations of the strength of the pump noise, the coupling constant and the difference of pump parameters have been investigated. The results show the following. (i) The pump noise dramatically affects the mode competition. (ii) The mode competition is quite sensitive to changing of the coupling constant near the line center. (iii) The mode competition gets stronger and stronger with increasing absolute value of the difference of pump parameters.

scholarly journals Estimating signal and noise of time-resolved X-ray solution scattering data at synchrotrons and XFELs

2020 ◽  
Vol 27 (3) ◽  
pp. 633-645
Author(s):  
Jungmin Kim ◽  
Jong Goo Kim ◽  
Hosung Ki ◽  
Chi Woo Ahn ◽  
Hyotcherl Ihee
Keyword(s):  
Quantum Noise ◽  
Structural Information ◽  
Signal To Noise Ratio ◽  
Liquid Solution ◽  
Solution Phase ◽  
Scattering Data ◽  
Time Resolved ◽  
X Ray ◽  
The Future ◽  
The Difference

Elucidating the structural dynamics of small molecules and proteins in the liquid solution phase is essential to ensure a fundamental understanding of their reaction mechanisms. In this regard, time-resolved X-ray solution scattering (TRXSS), also known as time-resolved X-ray liquidography (TRXL), has been established as a powerful technique for obtaining the structural information of reaction intermediates and products in the liquid solution phase and is expected to be applied to a wider range of molecules in the future. A TRXL experiment is generally performed at the beamline of a synchrotron or an X-ray free-electron laser (XFEL) to provide intense and short X-ray pulses. Considering the limited opportunities to use these facilities, it is necessary to verify the plausibility of a target experiment prior to the actual experiment. For this purpose, a program has been developed, referred to as S-cube, which is short for a Solution Scattering Simulator. This code allows the routine estimation of the shape and signal-to-noise ratio (SNR) of TRXL data from known experimental parameters. Specifically, S-cube calculates the difference scattering curve and the associated quantum noise on the basis of the molecular structure of the target reactant and product, the target solvent, the energy of the pump laser pulse and the specifications of the beamline to be used. Employing a simplified form for the pair-distribution function required to calculate the solute–solvent cross term greatly increases the calculation speed as compared with a typical TRXL data analysis. Demonstrative applications of S-cube are presented, including the estimation of the expected TRXL data and SNR level for the future LCLS-II HE beamlines.

The Cramer–Rao lower bound in a non-AWGN model for the affine phase retrieval

2021 ◽  
pp. 2050089
Author(s):  
Zhitao Zhuang ◽  
Kaixin Wang
Keyword(s):  
Lower Bound ◽  
Mean Square Error ◽  
Gaussian Noise ◽  
Phase Retrieval ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Mean Square ◽  
Cramer Rao Lower Bound ◽  
The Difference

In this paper, we derive the Cramer–Rao lower bound (CRLB) in a non-additive white Gaussian noise (AWGN) model for the affine phase retrieval (APR) and simulate the difference of CRLB and mean square error produced by PhaseLift of phase retrieval and APR in AWGN and non-AWGN cases.

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