Fault-tolerant quantum information processing with flawed qubits and gates requires highly efficient, quantum non-demolition (QND) qubit readout. In superconducting circuits, qubit readout using coherent light with fidelity above 99% has been achieved by using quantum-limited parametric amplifiers such as the Josephson Parametric Converter (JPC). However, further improvement of such measurement is fundamentally limited by the vacuum fluctuations of the coherent light used for readout. In this work we measure a transmon qubit/cavity system with an unbalanced two-mode squeezed light interferometer formed from two JPCs. The first amplifier generates two-mode squeezed vacuum at its output, which is coherently recombined by the second amplifier after one branch is shifted and displaced by the transmon's state after it interacts with the qubit/cavity system on one arm of the interferometer. We have observed a 31% improvement in power Signal-to-Noise Ratio (SNR) of projective readout compared to that of coherent light readout in the same system. To investigate the quantum properties of the two-mode squeezed light in the system, we also studied weak measurement and found, surprisingly, that tuning the interferometer to be as unprojective as possible was associated with an increase in the quantum efficiency of our readout relative to the optimum setting for projective measurement. These enhancements may enable remote entanglement with lower efficiency components in a system with qubits in both arms of the interferometer.
Fisher-Information Recovery in Superconducting-Qubit Magnetometry with Squeezed-Microwave Readout
Institute of Quantum Materials and Physics, Henan Academy of Sciences（河南省科学院量子材料与物理研究所）；Department of Physics, Central China Normal University（华中师范大学物理学院）；State Key Laboratory of Mathematical Engineering and Advanced Computing（数学工程与先进计算国家重点实验室）；Quantum Information Institute, School of Physics and Laboratory of Zhongyuan Light, Zhengzhou University（郑州大学物理学院量子信息研究所与中原之光实验室）
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.
According to quantum theory the interactions between physical systems are quantized. As a direct consequence, measurement sensitivities are fundamentally limited by quantization noise, or just `quantum noise' in short. Furthermore, Heisenberg's Uncertainty Principle demands measurement back-action for some observables of a system if they are measured repeatedly. In both respects, squeezed states are of high interest since they show a `squeezed' uncertainty, which can be used to improve the sensitivity of measurement devices beyond the usual quantum noise limits including those impacted by quan…
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 si…
A Michelson-type interferometer with two-mode squeezed coherent state input is considered. Such an interferometer has a better phase sensitivity over the shot-noise limit by a factor of $e^{2r}$, where $r$ is the squeezing parameter [Phys. Rev. A 102,022614 (2020)]. We show that when photon loss and noise in the two arms is asymmetric an optimal choice of the squeezing angle can allow improvement in phase sensitivity without any increase in input or pump power. In particular, when loss occurs only in one arm of the interferometer, we can have improvement in phase sensitivity for photon loss up…
Control over the spectral properties of the bright squeezed vacuum (BSV), a highly multimode non-classical macroscopic state of light that can be generated through high-gain parametric down conversion, is crucial for many applications. In particular, in several recent experiments BSV is generated in a strongly pumped SU(1,1) interferometer to achieve phase supersensitivity, perform broadband homodyne detection, or tailor the frequency spectrum of squeezed light. In this work, we present an analytical approach to the theoretical description of BSV in the frequency domain based on the Bloch-Mess…
Over the years, quite a few proposals have been put forward by various groups to exploit the Stern-Gerlach effect to create stable macroscopic spatial superpositions between micron-sized neutral test masses over appreciably long time scales. One such proposal put forward by Bose et al. and co-workers in 2017 uses this idea to show that two masses cannot be gravitationally entangled if not for the presence of a quantum coherent mediator. A key aspect of this approach involves the measure of the visibility of the SG-interferometer, a quantity that provides an estimate of the degree of spin coher…
Photon counting measurement has been regarded as the optimal measurement scheme for phase estimation in the squeezed-state interferometry, since the classical Fisher information equals to the quantum Fisher information and scales as $\bar{n}^2$ for given input number of photons $\bar{n}$. However, it requires photon-number-resolving detectors with a large enough resolution threshold. Here we show that a collection of $N$-photon detection events for $N$ up to the resolution threshold $\sim \bar{n}$ can result in the ultimate estimation precision beyond the shot-noise limit. An analytical formul…
We theoretically present the quantum Cramér-Rao bounds (QCRB) of an SU(1,1) interferometer for Gaussian states input with and without the internal photonic losses. The phase shifts in the single arm and in the double arms are studied and the corresponding analytical expressions of quantum Fisher information with Gaussian input states are presented. Different from the traditional Mach-Zehnder interferometer, the QCRB of single arm case is slightly higher or lower than that of double arms case depending on the input states. With a fixed mean photon number and for pure Gaussian state input, the o…
The sensitivity of laser interferometers used for the detection of gravitational waves (GWs) is limited by quantum noise of light. An improvement is given by light with squeezed quantum uncertainties, as employed in the GW detector GEO600 since 2010. To achieve simultaneous noise reduction at all signal frequencies, however, the spectrum of squeezed states needs to be processed by 100m-scale low-loss optical filter cavities in vacuum. Here, we report on the proof-of-principle of an interferometer setup that achieves the required processed squeezed spectrum by employing Einstein-Podolsky-Rosen …
Bright squeezed vacuum, a promising tool for quantum information, can be generated by high-gain parametric down-conversion. However, its frequency and angular spectra are typically quite broad, which is undesirable for applications requiring single-mode radiation. We tailor the frequency spectrum of high-gain parametric down-conversion using an SU(1,1) interferometer consisting of two nonlinear crystals with a dispersive medium separating them. The dispersive medium allows us to select a narrow band of the frequency spectrum to be exponentially amplified by high-gain parametric amplification. …
We theoretically study the phase sensitivity of the SU(1,1) interferometer with a coherent light together with a squeezed vacuum input case using the method of homodyne. We find that the homodyne detection has better sensitivity than the intensity detection under this input case. For a certain intensity of coherent light (squeezed light) input, the relative phase sensitivity is not always better with increasing the squeezed strength (coherent light strength). The phase sensitivity can reach the Heisenberg limit only under a certain moderate parameter interval, which can be realized with curren…
We study the phase sensitivity in the conventional $SU(2)$ and nonconventional $SU(1,1)$ interferometers with the coherent and squeezed vacuum input state via the quantum Cramer-Rao bound. We explicitly construct the detection scheme that gives the optimal phase sensitivity. For practical purposes, we show that in the presence of photon loss, both interferometers with proper homodyne detections, are nearly optimal. We also find that unlike the coherent state and squeezed vacuum state, the effects of the imperfect detector on the phase sensitivity cannot be asymptotically removed for a generic …
We propose a method for tailoring the frequency spectrum of bright squeezed vacuum by generating it in a nonlinear interferometer, consisting of two down-converting nonlinear crystals separated by a dispersive medium. Due to a faster dispersive spreading of higher-order Schmidt modes, the spectral width of the radiation at the output is reduced as the length of the dispersive medium is increased. Preliminary results show 30\% spectral narrowing.
Only a few years ago, it was realized that the zero-area Sagnac interferometer topology is able to perform quantum nondemolition measurements of position changes of a mechanical oscillator. Here, we experimentally show that such an interferometer can also be efficiently enhanced by squeezed light. We achieved a nonclassical sensitivity improvement of up to 8.2 dB, limited by optical loss inside our interferometer. Measurements performed directly on our squeezed-light laser output revealed squeezing of 12.7 dB. We show that the sensitivity of a squeezed-light enhanced Sagnac interferometer can …
The quantum Fisher information for a two-mode, Gaussian product state in an interferometer subject to photon loss is studied. We obtain the quantum Cramer-Rao bound on the achievable precision in phase estimation using such states. The scaling of the measurement precision with the mean photon number for such input product states is compared to the limited scaling for dual squeezed vacuum states and for dual squeezed, displaced vacuum states.
The use of an interferometer to perform an ultra-precise parameter estimation under noisy conditions is a challenging task. Here we discuss nearly optimal measurement schemes for a well known,sensitive input state, squeezed vacuum and coherent light. We find that a single mode intensity measurement, while the simplest and able to beat the shot-noise limit, is outperformed by other measurement schemes in the low-power regime. However, at high powers, intensity measurement is only outperformed by a small factor. Specifically, we confirm, that an optimal measurement choice under lossless conditio…
An all-fibre source of amplitude squeezed solitons utilizing the self-phase modulation in an asymmetric Sagnac interferometer is experimentally demonstrated. The asymmetry of the interferometer is passively controlled by an integrated fibre coupler, allowing for the optimisation of the noise reduction. We have carefully studied the dependence of the amplitude noise on the asymmetry and the power launched into the Sagnac interferometer. Qualitatively, we find good agreement between the experimental results, a semi-classical theory and earlier numerical calculations [Schmitt etl.al., PRL Vol. 81…
We report on the generation of polarization squeezing of intense, short light pulses using an asymmetric fiber Sagnac interferometer. The Kerr nonlinearity of the fiber is exploited to produce independent amplitude squeezed pulses. The polarization squeezing properties of spatially overlapped amplitude squeezed and coherent states are discussed. The experimental results for a single amplitude squeezed beam are compared to the case of two phase-matched, spatially overlapped amplitude squeezed pulses. For the latter, noise variances of -3.4dB below shot noise in the S0 and the S1 and of -2.8dB i…
Quantum optical states which have no coherent amplitude, such as squeezed vacuum states, can not rely on standard readout techniques to generate error signals for control of the quadrature phase. Here we investigate the use of asymmetry in the quadrature variances to obtain a phase-sensitive readout and to lock the phase of a squeezed vacuum state, a technique which we call noise locking (NL). We carry out a theoretical derivation of the NL error signal and the associated stability of the squeezed and anti-squeezed lock points. Experimental data for the NL technique both in the presence and ab…
Application of frequency-dependent squeezed vacuum improves the force sensitivity of optomechanical interferometer beyond the standard quantum limit by a factor of $e^{-r}$, where $r$ is the squeezing parameter. In this work, we show that the application of squeezed light along with quantum optical restoring force can enhance the sensitivity beyond the standard quantum limit by a factor of $\sqrt{e^{-2r}ζ/4Δ}$, where $0< ζ/Δ<1$, with $ζ$ as the optomechanical cavity decay rate and $Δ$ as the detuning between cavity eigenfrequency and driving field. The technique described in this article is re…
We propose a multi-parameter quantum metrological protocol based on a Mach-Zehnder interferometer with a squeezed vacuum input state and an anti-squeezing operation at one of its output channels. A simple and intuitive geometrical picture of the state evolution is provided by the marginal Wigner functions of the state at each interferometer output channel. The protocol allows to detect the value of the sum $β=\frac{1}{2}(φ_1+φ_2)+θ_\mathrm{in}-θ_\mathrm{out}$, of the relative phase $θ_\mathrm{in}-θ_\mathrm{out}$ between the two squeezers, and the average of the phase delays $φ_1,φ_2$ in the tw…
We study in detail a system of two interferometers aimed to the detection of extremely faint phase-fluctuations. This system can represent a breakthrough for detecting a faint correlated signal that would remain otherwise undetectable even using the most sensitive individual interferometric devices, that are limited by the shot noise. If the two interferometers experience identical phase-fluctuations, like the ones introduced by the so called "holographic noise", this signal should emerge if their output signals are correlated, while the fluctuations due to shot noise and other independent con…
We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities, and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circui…
This paper has been withdrawn. It is based on numerical results limited by computing resources to N=3000 atoms. Using a newly understood geometric method we find that the observed scaling with N saturates at around N=7000 or even higher. In light of this new finding we withdraw the paper and will submit a revised manuscript reflecting our new understanding.
We study a sensor network of distributed Mach-Zehnder interferometers (MZIs) for the parallel (simultaneous) estimation of an arbitrary number $d \geq 1$ of phase shifts. The scheme uses a squeezed-vacuum state that is split between $d$ modes by a quantum circuit (QC). Each output mode of the QC is the input of one of $d$ MZIs, the other input of each MZI being a coherent state. In particular, ${\it i}$) we identify the optimal configuration of the sensor network that allows the estimation of any linear combination of the $d$ phases with maximal sensitivity. The protocol overcomes the shot-noi…
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so called `dark port case', when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (`dark port'). For this case it had been suggested that signal amplification is possible without concurrent noise a…
The LIGO-II gravitational-wave interferometers (ca. 2006--2008) are designed to have sensitivities at about the standard quantum limit (SQL) near 100 Hz. This paper describes and analyzes possible designs for subsequent, LIGO-III interferometers that can beat the SQL. These designs are identical to a conventional broad-band interferometer (without signal recycling), except for new input and/or output optics. Three designs are analyzed: (i) a "squeezed-input interferometer" (conceived by Unruh based on earlier work of Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle i…
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 ne…
We report on the generation of a stable continuous-wave low-frequency squeezed vacuum field with a squeezing level of $3.8\pm0.1$ dB at 1064 nm, the wavelength at which laser interferometers for gravitational wave (GW) detection operate, using periodically poled KTiOPO$_4$ (PPKTP) in a sub-threshold optical parametric oscillator. PPKTP has the advantages of higher nonlinearity, smaller intra-crystal and pump-induced seed absorption, user-specified parametric down-conversion temperature, wider temperature tuning range, and lower susceptibility to thermal lensing over alternative nonlinear mater…
Interferometers are crucial for precision measurements, including gravitational waves, laser ranging, radar, and imaging. The phase sensitivity, the core parameter, can be quantum-enhanced to break the standard quantum limit (SQL) using quantum states. However, quantum states are highly fragile and quickly degrade with losses. We design and demonstrate a quantum interferometer utilizing a beam splitter with a variable splitting ratio to protect the quantum resource against environmental impacts. The optimal phase sensitivity can reach the quantum Cramér-Rao bound of the system. This quantum in…
We address the performance of an interferometric setup in which a squeezed single photon interferes at a beam splitter with a coherent state. Our analysis in based on both the quantum Fisher information and the sensitivity when a Mach-Zehnder setup is considered and the difference photocurrent is detected at the output. We compare our results with those obtained feeding the interferometer with a squeezed vacuum (with the same squeezing parameter of the squeezed single photon) and a coherent state in order to have the same total number of photons circulating in the interferometer. We find that …
It is shown in the present Letter that the quantum noise due to high laser intensities in Michelson interferometer for gravitational waves detection can be reduced by sending squeezed vacuum states to the 'dark' port of the interferometer. The experimental details of such physical system have been described in a recent article by Barak and Ben-Aryeh (JOSA-B, 25, 361(2008)). In another very recent article by Voronov and Weyrauch (Phys. Rev.A 81, 053816 (2010)) they have followed our methods for treating the same physical system, and have pointed out an error in the sign of one of our expression…
We present a protocol for measuring the quadrature of a harmonic oscillator (HO). The HO is coupled to a qubit, with an interaction modulated by the qubit control and effectively proportional to the HO quadrature $I$. Repeated measurement of the qubit leads to gradually increasing information on the quadrature $I$, leading to squeezing. We derive an analytical formula for the quadrature variance, $(ΔI)^2 = 1/(1+4ϕ^2 s)$, with $ϕ$ the product of interaction strength and interaction time and $s$ the number of repetitions of the measurement. We discuss the robustness of this scheme against decohe…
We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are function of the internal phase-shift of the interferometer, with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing function of the input squeezing parameter. A couple of squeezed vacuum at the input leads to maximum entangled state at the output. The fringes visibilities resulting from measuring the coincidence counting rat…
We present the observation of optical fields carrying squeezed vacuum states at sideband frequencies from 10Hz to above 35MHz. The field was generated with type-I optical parametric oscillation below threshold at 1064nm. A coherent, unbalanced classical modulation field at 40MHz enabled the generation of error signals for stable phase control of the squeezed vacuum field with respect to a strong local oscillator. Broadband squeezing of approximately -4dB was measured with balanced homodyne detection. The spectrum of the squeezed field allows a quantum noise reduction of ground-based gravitatio…
Here we report on the realization of a Michelson-Sagnac interferometer whose purpose is the precise characterization of the motion of membranes showing significant light transmission. Our interferometer has a readout noise spectral density (imprecision) of 3E-16 m/sqrt(Hz) at frequencies around the fundamental resonance of a SiN_x membrane at about 100 kHz, without using optical cavities. The readout noise demonstrated is more than 16 dB below the peak value of the membrane's standard quantum limit (SQL). This reduction is significantly higher than those of previous works with nano-wires [Teuf…
We present a method for determining the phase and contrast of a single shot of an atom interferometer. The application of a phase shear across the atom ensemble yields a spatially varying fringe pattern at each output port, which can be imaged directly. This method is broadly relevant to atom interferometric precision measurement, as we demonstrate in a 10 m Rb-87 atomic fountain by implementing an atom interferometric gyrocompass with 10 millidegree precision.
The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. The complete tomographic reconstruction of the state of light requires the ability to readout arbitrary quadratures. Here we demonstrate such a readout by applying a balanced homodyne detector to an interferometric position measurement of a thermally excited high-Q silicon nitride membrane in a Michelson-Sagnac interferome…
The accuracy of microwave measurements is not only critical for applications in telecommunication and radar, but also for future quantum computers. Qubit technologies such as superconducting qubits or spin qubits require detecting minuscule signals, typically achieved by reflecting a microwave tone off a resonator that is coupled to the qubit. Noise from cabling and amplification, e.g. from temperature variations, can be detrimental to readout fidelity. We present an approach to detect phase and amplitude changes of a device under test based on the differential measurement of microwave tones g…
A method for mitigating the readout delay characteristic of Bragg-based atom interferometry is presented, utilizing an asymmetric Mach-Zehnder interferometer sequence to generate spatial fringes that are read out while still overlapped. The time of flight after the final beamsplitter is engineered to facilitate constructive overlap of the fringes on the output states. A noise analysis performed using a precision atom interferometer is presented, comparing the traditional separated symmetric scheme with that of the separated and overlapped asymmetric scheme showing no significant increase in sh…
