Enhancement of Sensitivity by Initial Phase Matching in SU(1,1) Interferometers

We derive a general phase-matching condition(PMC) for enhancement of sensitivity in SU(1,1) interferometers. Under this condition, the quantum Fisher information(QFI) of two-mode SU(1,1) interferometry becomes maximal with respect to the relative phase of two modes, for the case of an arbitrary state in one input port and an even(odd) state in the other port, and the phase sensitivity is enhanced. We also find that optimal parameters can let the QFI in some areas achieve the Heisenberg limit for both pure and mixed initial states. As examples, we consider several input states: coherent and even coherent states, squeezed vacuum and even coherent states, squeezed thermal and even coherent states. Furthermore, in the realistic scenario of the photon loss channel, we investigate the effect of photon losses on QFI with numerical studies. We find the PMC remains unchanged and is not affected by the transmission coefficients for the above input states. Our results suggest that the PMC can exist in various kinds of interferometers and the phase-matching is robust to even strong photon losses.     

Tolerance-enhanced SU(1,1) interferometers using asymmetric gain

SU(1,1) interferometers play an important role in quantum metrology. Previous studies focus on various inputs and detection strategies with symmetric gain. In this paper, we analyze a modified SU(1,1) interferometer using asymmetric gain. Two vacuum states are used as the input and on-off detection is performed at the output. In a lossless scenario, symmetric gain is the optimal selection and the corresponding phase sensitivity can achieve the Heisenberg limit as well as the quantum Cramer-Rao bound. In addition, we analyze the phase sensitivity with symmetric gain in the lossy scenario. The phase sensitivity is sensitive to internal losses but extremely robust against external losses. We address the optimal asymmetric gain and the results suggest that this method can improve the tolerance to internal losses. Our work may contribute to the practical development of quantum metrology.     

The Phase Sensitivities for Different Phase-Shift Configurations in an SU(1,1) Interferometer

We theoretically study the phase sensitivities of two different phase-shift configurations in an SU(1,1)interferometer with coherent ■ squeezed vacuum states.According to quantum Cramér-Rao theorem,we analytically obtain the ultimate phase sensitivities for two types of phase shift accumulating in one-and two-arm.Compared with the case of one-arm phase shift,the model with phase shift encoding in both arms may provide a better sensitivity when the strength of squeezed vacuum state is large enough.Furthermore,we discuss the achievable sensitivities with the homodyne measurement by invoking of error-propagation formula.In addition,we study the effect of internal and outernal photon losses on the phase sensitivity of the SU(1,1) interferometer and find that the unbalanced interferometer is helpful to improve precision even with high external losses.     

叠加的奇偶SU(1,1)相干态的统计性质

研究了将两个SU(1,1)相干态｜ζ,k〉和｜ζ,k〉叠加起来得到的新的量子态的统计性质．偶SU(1,1)相干态｜ζ,1/4〉和奇SU(1,1)相干态｜ζ,3/4〉分别对应于压缩真空态和压缩单光子数态．适当选取SU(1,1)态的相位角和叠加时的相对相位,得到的新的量子态比单个SU(1,1)相干态表现出大大增强的正交分量压缩和光子反群聚效应．也说明了怎样准备这样的叠加态． 关键词：     

Phase estimation of phase shifts in two arms for an SU(1,1) interferometer with coherent and squeezed vacuum states

We theoretically study the quantum Fisher information(QFI) of the SU(1,1) interferometer with phase shifts in two arms by coherent ? squeezed vacuum state input, and give the comparison with the result of phase shift only in one arm.Different from the traditional Mach–Zehnder interferometer, the QFI of single-arm case for an SU(1,1) interferometer can be slightly higher or lower than that of two-arm case, which depends on the intensities of the two arms of the interferometer.For coherent ? squeezed vacuum state input with a fixed mean photon number, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other.     

UNCORRELATED TWO-MODE SU(1,1) COHERENT STATES

We have constructed a new kind of two-mode bosonic realization of SU(1,1) Lie algebra, on the basis of which the SU(1,1) generalized coherent states in the two-mode Fock space are derived. These two-mode SU(1,1) coherent states, which are called uncorrelated two-mode SU(1,1) coherent states, include three special cases. For these states, we study the mean photon number distribution and their non-classical properties, which are photon anti-bunching, violations of Cauchy－Schwarz inequality and two-mode squeezing.     

非线性孪相干态的光子统计性质

利用f振子的湮没算符和产生算符的逆算符的性质，得到了SU(1，1)李代数的两个双模非厄密实现，在此基础上引入了两种非线性孪相干态，并讨论了它们的光子统计性质和相位特性。     

Enhanced phase sensitivity with a nonconventional interferometer and nonlinear phase shifter

We propose a theoretical scheme of an enhanced phase sensitivity by introducing a nonlinear phase shifter to the nonconventional interferometer consisting of a balanced beam splitter (BBS) and an optical parameter amplifier (OPA), a modified nonlinear interferometer (MNI). Then we use coherent state and even coherent state as inputs and homodyne detection at one output port of the MNI for phase sensitivity, both without and with photon losses. We find that the nonlinear phase shifter can not only improve phase sensitivity, but also significantly resist the decoherence from photon losses. In comparison to both the BBS+OPA scheme with linear phase shifter and the traditional Mach–Zehnder interferometer with nonlinear one, the phase sensitivity of the MNI scheme shows the best performance. It is interesting that the nonlinear phase shifter can stimulate potential of the OPA, although there is no improvement in signal-to-noise ratio beyond standard quantum limit for the BBS+OPA scheme with a linear phase shifter.     

光和原子关联与量子计量

物理量的测量与单位标准的统一推动了计量学的发展.量子力学的建立,激光技术的发明以及原子与分子物理学的发展,在原理与技术上进一步刷新了计量学的研究内涵,特别是激光干涉与原子频标技术的发展,引起了计量学革命性的飞跃.基于激光干涉的引力波测量、激光陀螺仪,基于原子干涉的原子钟、原子陀螺仪等精密测量技术相继诞生,一个以量子物理为基础,探索与开拓物理量精密测量方法与技术的新的科学分支——量子计量学(Quantum Metrology)已然兴起.干涉是计量学中最常用的相位测量方法.量子干涉技术,其相位测量精度能够突破标准量子极限的限制,是量子计量学与量子测量技术的核心研究内容.本文重点介绍近几年我们在量子干涉方面所取得的新开拓与新发展,主要内容包括基于原子系综中四波混频过程的SU(1,1)型光量子关联干涉仪和基于原子系综中拉曼散射过程的光-原子混合干涉仪.     

Optical enhanced interferometry with two-mode squeezed twin-Fock states and parity detection

We theoretically investigate the quantum enhanced metrology using two-mode squeezed twin-Fock states and parity detection. Our results indicate that, for a given initial squeezing parameter, compared with the two-mode squeezed vacuum state, both phase sensitivity and resolution can be enhanced when the two-mode squeezed twin-Fock state is considered as an input state of a Mach–Zehnder interferometer. Within a constraint on the total photon number, although the two-mode squeezed vacuum state gives the better phase sensitivity when the phase shift φ to be estimated approaches to zero, the phase sensitivity offered by these non-Gaussian entangled Gaussian states is relatively stable with respect to the phase shift itself. When the phase shift slightly deviates from φ= 0, the phase sensitivity can be still enhanced by the two-mode squeezed twin-Fock state over a broad range of the total mean photon number where the phase uncertainty is still below the quantum standard noise limit. Finally, we numerically prove that the quantum Cramer–Rao bound can be approached with the parity detection.     

The parity operator in quantum optical metrology

Photon number states are assigned a parity of +1 if their photon number is even and a parity of ?1 if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable although it has no classical analogue, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the parity operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenberg limit sensitivities are expected to eventually play an important role in attempts to detect gravitational waves in interferometric detection systems such as LIGO and VIRGO.     

Enhanced phase sensitivity of an SU(1,1) interferometer with displaced squeezed vacuum light

We study the phase sensitivity of an SU(1,1) interferometer with two input beams in the displaced squeezed vacuum state and the coherent state, respectively. We find that there exists an optimal squeezing fraction of the displaced squeezed vacuum state that optimizes the phase sensitivity. We also examine the effects of some factors, including the loss, mean photon number of the input beams and amplitude gain of the optical parameter amplifiers, on the optimal squeezing fraction so that we can choose the optimal values to enhance the phase sensitivity.     

Science as social history

Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is possible classically, and also exceeds what was once thought to be possible quantum mechanically. The primary idea is to exploit quantum effects to beat the shot-noise limit in metrology and the Rayleigh diffraction limit in imaging and sensing. Quantum optical metrology has received a boost in recent years with an influx of ideas from the rapidly evolving field of optical quantum information processing. Both areas of research exploit the creation and manipulation of quantum-entangled states of light. We will review some of the recent theoretical and experimental advances in this exciting new field of quantum optical metrology, focusing on examples that exploit a particular two-mode entangled photon state – the High-N00N state.     

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed. PACS Numbers: 02.20.Sv, 03.65.-w, 03.65.Fd     

Quantum multiparameter estimation with multi-mode photon catalysis entangled squeezed state

We propose a method to generate the multi-mode entangled catalysis squeezed vacuum states (MECSVS) by embedding the cross-Kerr nonlinear medium into the Mach−Zehnder interferometer. This method realizes the exchange of quantum states between different modes based on Fredkin gate. In addition, we study the MECSVS as the probe state of multi-arm optical interferometer to realize multi-phase simultaneous estimation. The results show that the quantum Cramer−Rao bound (QCRB) of phase estimation can be improved by increasing the number of catalytic photons or decreasing the transmissivity of the optical beam splitter using for photon catalysis. In addition, we also show that even if there is photon loss, the QCRB of our photon catalysis scheme is lower than that of the ideal entangled squeezed vacuum states (ESVS), which shows that by performing the photon catalytic operation is more robust against photon loss than that without the catalytic operation. The results here can find applications in quantum metrology for multiparatmeter estimation.     

Negativity of Wigner function and phase sensitivity of an SU(1,1) interferometer

Both the negativity of Wigner function and the phase sensitivity of an SU(1,1) interferometer are investigated in this paper. In the case that the even coherent state and squeezed vacuum state are input into the interferometer, the Heisenberg limit can be approached with parity detection. At the same time, the negativity volume of Wigner function of detection mode comes entirely from the input state and varies periodically with the encoding phase. In addition, the negativity volume of Wigner function is positively correlated with the phase sensitivity of the SU(1,1) interferometer. The positive correlation may mean that the non-classicality indicated by negative Wigner function is a kind of resource that can verify some related research results of phase estimation.     

两参数变形量子代数SU(1,1)q,s的相干态及其性质

利用SU(1,1)_q,s量子代数的两参数变形振子构造出归一化的SU(1,1)_q,s相干态,证明了SU(1,1)_q,s量子代数的表示基是正交的,并讨论了它的相干态的归一性和完备性。指出(SU(1,1)_q,s相干态的相干性受参数q、s的影响。     

双模场与原子相互作用中的量子纠缠和内禀退相干

通过求解系统的Milburn方程，研究了两能级原子与双模SU(1,1)相干态光场发生相互作用系统中，原子与场的纠缠及双模SU(1,1)相干态场的模间纠缠随时间的演化问题，讨论了内禀退相干、双模光子数差等对纠缠度的影响.结果表明，存在内禀退相干时，随着时间的演化，场-原子纠缠逐渐减小到一个确定值，而模间纠缠逐渐增大到一个确定值，两者演化的最终值只取决于双模光子数差和平均光子数，而与内禀退相干因子无关. 关键词： Milburn理论 SU(1 1)相干态 量子约化熵 量子相对熵     

Super-sensitive phase estimation with coherent boosted light using parity measurements

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach-Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer-Rao bound than the pure active(e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves[Phys. Rev. D 23 1693(1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves' scheme.     

Maximally Entangled SU(1,1) Semi Coherent States

In this paper, we consider a special type of maximally entangled states namely by entangled SU(1,1) semi coherent states by using SU(1,1) semi coherent states(SU(1,1) Semi CS). The entanglement characteristics of these entangled states are studied by evaluating the concurrence.We investigate some of their nonclassical properties,especially probability distribution function,second-order correlation function and quadrature squeezing . Further, the quasiprobability distribution functions (Q-functions) is discussed.