Quantum states of light can enable sensing configurations with sensitivities beyond the shot-noise limit (SNL). In order to better take advantage of available quantum resources and obtain the maximum possible sensitivity, it is necessary to determine
fundamental sensitivity limits for different possible configurations for a given sensing system. Here, due to their wide applicability, we focus on optical resonance sensors, which detect a change in a parameter of interest through a resonance shift. We compare their fundamental sensitivity limits set by the quantum Cramer-Rao bound (QCRB) based on the estimation of changes in transmission or phase of a probing bright two-mode squeezed state (bTMSS) of light. We show that the fundamental sensitivity results from an interplay between the QCRB and the transfer function of the system. As a result, for a resonance sensor with a Lorentzian lineshape a phase-based scheme outperforms a transmission-based one for most of the parameter space; however, this is not the case for lineshapes with steeper slopes, such as higher order Butterworth lineshapes. Furthermore, such an interplay results in conditions under which the phase-based scheme provides a higher sensitivity than the transmission-based one but a smaller degree of quantum enhancement. We also study the effect of losses external to the sensor on the degree of quantum enhancement and show that for certain conditions probing with a classical state can provide a higher sensitivity than probing with a bTMSS. Finally, we discuss detection schemes, namely optimized intensity-difference and optimized homodyne detection, that can achieve the fundamental sensitivity limits even in the presence of external losses.
The ability to deterministically generate genuine multi-partite entanglement is fundamental for the advancement of quantum information science. We show that the interaction between entangled twin beams of light and an atomic ensemble under conditions
for electromagnetically induced transparency leads to the generation of genuine hybrid tri-partite entanglement between the two input fields and the atomic ensemble. In such a configuration, the system is driven through dissipation to a steady state given by the hybrid entangled state. To show the presence of the genuine hybrid entanglement, we introduce a new approach to treat the atomic operators that makes it possible to show a violation of a tri-partite entanglement criterion based on the properties of the two optical fields and collective properties of the atomic ensemble. Additionally, we show that while each of the input optical fields does not exhibit single beam quadrature squeezing, as the fields propagate through the atomic medium their individual quadratures can become squeezed and in some cases oscillate between the presence and absence of squeezing. Finally, we propose a technique to characterize the tri-partite entanglement through joint measurements of the fields leaving the atomic medium, making such an approach experimentally accessible.
Spatial entanglement is at the heart of quantum enhanced imaging applications and high-dimensional quantum information protocols. In particular, for imaging and sensing applications, quantum states with a macroscopic number of photons are needed to p
rovide a real advantage over the classical state-of-the-art. We demonstrate the Einstein-Podolsky-Rosen (EPR) paradox in its original position and momentum form with bright twin beams of light by showing the presence of EPR spatial (position-momentum) entanglement. An electron-multiplying charge-coupled-device camera is used to record images of the bright twin beams in the near and far field regimes to achieve an apparent violation of the uncertainty principle by more than an order of magnitude. We further show that the presence of quantum correlations in the spatial and temporal degrees of freedom leads to spatial squeezing between the spatial fluctuations of the bright twin beams in both the near and far fields. This provides another verification of the spatial entanglement and points to the presence of hyperentanglement in the bright twin beams.
Electromagnetically induced transparency (EIT) is a well-known phenomenon due in part to its applicability to quantum devices such as quantum memories and quantum gates. EIT is commonly modeled with a three-level lambda system due to the simplicity o
f the calculations. However, this simplified model does not capture all the physics of EIT experiments with real atoms. We present a theoretical study of the effect of two closely-spaced excited states on EIT and off-resonance Raman transitions. We find that the coherent interaction of the fields with two excited states whose separation is smaller than their Doppler broadened linewidth can enhance the EIT transmission and broaden the width of the EIT peak. However, a shift of the two-photon resonance frequency for systems with transitions of unequal dipole strengths leads to a reduction of the maximum transparency that can be achieved when Doppler broadening is taken into account even under ideal conditions of no decoherence. As a result, complete transparency cannot be achieved in a vapor cell. Only when the separation between the two excited states is of the order of the Doppler width or larger can complete transparency be recovered. In addition, we show that off-resonance Raman absorption is enhanced and its resonance frequency is shifted. Finally, we present experimental EIT measurements on the D1 line of $^{85}$Rb that agree with the theoretical predictions when the interaction of the fields with the four levels is taken into account.
Squeezed states of light have received renewed attention due to their applicability to quantum-enhanced sensing. To take full advantage of their reduced noise properties to enhance atomic-based sensors, it is necessary to generate narrowband near or
on atomic resonance single-mode squeezed states of light. We have previously generated bright two-mode squeezed states of light, or twin beams, that can be tuned to resonance with the D1 line of $^{87}$Rb with a non-degenerate four-wave mixing (FWM) process in a double-lambda configuration in a $^{85}$Rb vapor cell. Here we report on the use of feedforward to transfer the amplitude quantum correlations present in the twin beams to a single beam for the generation of single-mode amplitude squeezed light. With this technique we obtain a single-mode squeezed state with a squeezing level of $-2.9pm0.1$ dB when it is tuned off-resonance and a level of $-2.0pm 0.1$ dB when it is tuned on resonance with the D1 $F=2$ to $F=2$ transition of $^{87}$Rb.
Squeezed states of light have found their way into a number of applications in quantum-enhanced metrology due to their reduced noise properties. In order to extend such an enhancement to metrology experiments based on atomic ensembles, an efficient l
ight-atom interaction is required. Thus, there is a particular interest in generating narrow-band squeezed light that is on atomic resonance. This will make it possible not only to enhance the sensitivity of atomic based sensors, but also to deterministically entangle two distant atomic ensembles. We generate bright two-mode squeezed states of light, or twin beams, with a non-degenerate four-wave mixing (FWM) process in hot $^{85}$Rb in a double-lambda configuration. Given the proximity of the energy levels in the D1 line of $^{85}$Rb and $^{87}$Rb, we are able to operate the FWM in $^{85}$Rb in a regime that generates two-mode squeezed states in which both modes are simultaneously on resonance with transitions in the D1 line of $^{87}$Rb, one mode with the $F=2$ to $F=2$ transition and the other one with the $F=1$ to $F=1$ transition. For this configuration, we obtain an intensity difference squeezing level of $-3.5$ dB. Moreover, the intensity difference squeezing increases to $-5.4$ dB and $-5.0$ dB when only one of the modes of the squeezed state is resonant with the D1 $F=2$ to $F=2$ or $F=1$ to $F=1$ transition of $^{87}$Rb, respectively.
We show that it is possible to use the spatial quantum correlations present in twin beams to extract information about the shape of a mask in the path of one of the beams. The scheme, based on noise measurements through homodyne detection, is useful
in the regime where the number of photons is low enough that direct detection with a photodiode is difficult but high enough that photon counting is not an option. We find that under some conditions the use of quantum states of light leads to an enhancement of the sensitivity in the estimation of the shape of the mask over what can be achieved with a classical state with equivalent properties (mean photon flux and noise properties). In addition, we show that the level of enhancement that is obtained is a result of the quantum correlations and cannot be explained with only classical correlations.
We have observed a violation of the Cauchy-Schwarz inequality in the macroscopic regime by more than 8 standard deviations. The violation has been obtained while filtering out only the low frequency noise of the quantum-correlated beams that results
from the technical noise of the laser used to generate them. We use bright intensity-difference squeezed beams produced by four-wave mixing as the source of the correlated fields. We also demonstrate that squeezing does not necessarily imply a violation of the Cauchy-Schwarz inequality.
We present a new technique for the detection of two-mode squeezed states of light that allows for a simple characterization of these quantum states. The usual detection scheme, based on heterodyne measurements, requires the use of a local oscillator
with a frequency equal to the mean of the frequencies of the two modes of the squeezed field. As a result, unless the two modes are close in frequency, a high-frequency shot-noise-limited detection system is needed. We propose the use of a bichromatic field as the local oscillator in the heterodyne measurements. By the proper selection of the frequencies of the bichromatic field, it is possible to arbitrarily select the frequency around which the squeezing information is located, thus making it possible to use a low-bandwidth detection system and to move away from any excess noise present in the system.
We propose a scheme for quantum cryptography that uses the squeezing phase of a two-mode squeezed state to transmit information securely between two parties. The basic principle behind this scheme is the fact that each mode of the squeezed field by i
tself does not contain any information regarding the squeezing phase. The squeezing phase can only be obtained through a joint measurement of the two modes. This, combined with the fact that it is possible to perform remote squeezing measurements, makes it possible to implement a secure quantum communication scheme in which a deterministic signal can be transmitted directly between two parties while the encryption is done automatically by the quantum correlations present in the two-mode squeezed state.
