To enhance the phase sensitivity of Mach–Zehnder interferometers,we use a tunable phase shift before the light beams are injected into the interferometer.The analytical result of the optimal phase shift is obtained,w...To enhance the phase sensitivity of Mach–Zehnder interferometers,we use a tunable phase shift before the light beams are injected into the interferometer.The analytical result of the optimal phase shift is obtained,which only depends on the initial input states.For a non-zero optimal phase shift,the phase sensitivity of the interferometers in the output ports is always enhanced.We can achieve this enhancement for most states,including entangled and mixed states.The optimal phase shift is exhibited in three examples.Compared to previous methods,this scheme provides a general way to improve phase sensitivity and could find wide applications in optical phase estimations.展开更多
By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum sys...By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum system with highdimensional Hilbert space.However,the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet.Here,a practical method is presented to resolve the problem for the mixed-spin(s,1/2)system and describe the entanglement of the system.The system can be decomposed into two spins:spin-(s+1/2)and spin-(s−1/2)at the coupling bases,which can be regarded as independent spins.Besides,any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2)state and the other spin-(s−1/2)state.Thus,the whole initial state can be regarded as a state of a pseudo spin-1/2.In this way,the mixed spin decomposes into three spins.Therefore,the state can be represented by(2s+1)+(2s−1)+1=4s+1 sets of stars on a Bloch sphere.Finally,some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.展开更多
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...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.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11875231 and 11935012)the National Key Research and Development Program of China(Grant Nos.2017YFA0304202 and 2017YFA0205700)the Fundamental Research Funds for the Central Universities(Grant No.2018FZA3005)。
文摘To enhance the phase sensitivity of Mach–Zehnder interferometers,we use a tunable phase shift before the light beams are injected into the interferometer.The analytical result of the optimal phase shift is obtained,which only depends on the initial input states.For a non-zero optimal phase shift,the phase sensitivity of the interferometers in the output ports is always enhanced.We can achieve this enhancement for most states,including entangled and mixed states.The optimal phase shift is exhibited in three examples.Compared to previous methods,this scheme provides a general way to improve phase sensitivity and could find wide applications in optical phase estimations.
基金Project supported by the National Key Research and Development Program of China(Grant Nos.2017YFA0304202 and 2017YFA0205700)the National Natural Science Foundation of China(Grant No.11875231)the Fundamental Research Funds for the Central Universities,China(Grant No.2018FZA3005).
文摘By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum system with highdimensional Hilbert space.However,the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet.Here,a practical method is presented to resolve the problem for the mixed-spin(s,1/2)system and describe the entanglement of the system.The system can be decomposed into two spins:spin-(s+1/2)and spin-(s−1/2)at the coupling bases,which can be regarded as independent spins.Besides,any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2)state and the other spin-(s−1/2)state.Thus,the whole initial state can be regarded as a state of a pseudo spin-1/2.In this way,the mixed spin decomposes into three spins.Therefore,the state can be represented by(2s+1)+(2s−1)+1=4s+1 sets of stars on a Bloch sphere.Finally,some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.
基金Supported by the National Key Research and Development Program of China under Grant Nos.2017YFA0304202 and 2017YFA0205700the NSFC through Grant No.11875231the Fundamental Research Funds for the Central Universities through Grant No.2018FZA3005
文摘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.