Squeezed spin states possess unique quantum correlation or entanglement that are of significant promises for advancing quantum information processing and quantum metrology. In recent back to back publications [C. Gross et al, Nature 464, 1165 and Max F. Riedel et al, Nature 464, 1170Nature 464, (2010], reduced spin fluctuations are observed leading to spin squeezing at −8.2dB and −2.5dB respectively in two-component atomic condensates exhibiting one-axis-twisting interactions (OAT). The noise reduction limit for the OAT interaction scales as ∝ 1/N 2/3 , which for a condensate with N ∼ 10 3 atoms, is about 100 times below standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the OAT spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction ∝ 1/N , or an extra 10-fold improvement for N ∼ 10 3 .PACS numbers: 42.50.-p, 03.75.GgSqueezed spin states (SSS) [2,3] are entangled quantum states of a collection of spins in which the correlations among individual spins reduce quantum uncertainty of a particular spin component below the classical limit for uncorrelated particles [2]. Research in SSS is a topical area due to its significant applications in high-precision measurements [3][4][5][6][7][8][9][10] and in quantum information science [11][12][13][14][15]. Squeezed spin states were first introduced by Kitagawa and Ueda, who considered two ways to produce them. The simplest to implement uses a "one-axis twisting" (OAT) Hamiltonian, but the state it produces does not have ideal squeezing properties. A more complex approach uses a "two-axis twisting" (TAT) Hamiltonian and produces an improved state. Other mechanisms for producing SSS have also been investigated, especially those based on atom-photon interactions [16,17] and quantum non-demolition measurements [18][19][20][21].Atomic Bose-Einstein condensates are promising systems for observing spin squeezing. Assuming fixed spatial modes, condensed atoms are described by a collection of pseudo-spin 1/2 atoms, with spin up (|↑ ) and down (|↓ ) denoting the two internal states or spatial modes [12,[22][23][24][25]. The two recent experiments [4, 5] raise significant hope for reaching the theoretical limit of spin squeezing ∝ 1/N 2/3 with N the total number of atoms for the OAT model [2]. Both experiments utilize two internal hyperfine states of condensed atoms, with the OAT interaction cleverly constructed from binary atomic collisions, possibly accompanied by systematic and fundamental imperfections not confined to the two state/mode approximation. They can be further degraded by atomic decoherence and dissipation [4,5]. This Letter describes a readily implementable idea for improved spin squeezing in the two experiments. Given the reported OAT model parameters [4,5], we propose a coherent control scheme capable of transforming the OAT into the effective TAT spin squeezing, leading to a Heisenberg limited noise reduction ∝ 1/N , or a further 10 fold improvement for a condensate with ∼ 10 3 at...

We investigate the performance of entangled coherent state for quantum enhanced phase estimation. An exact analytical expression of quantum Fisher information is derived to show the role of photon losses on the ultimate phase sensitivity. We find a transition of the sensitivity from the Heisenberg scaling to the classical scaling due to quantum decoherence of the photon state. This quantum-classical transition is uniquely determined by the number of photons being lost, instead of the number of incident photons or the photon loss rate alone. Our results also reveal that a crossover of the sensitivity between the entangled coherent state and the NOON state can occur even for very small photon loss rate.

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A simple scheme for storage of spin squeezing in a two-component Bose-Einstein condensate is investigated by considering rapidly turning-off the external field at a time that maximal spin squeezing occurs. We show that strong reduction of spin fluctuation can be maintained in a nearly fixed direction. We explain the underlying physics using the phase model and present analytical expressions of the maximal-squeezing time and the corresponding squeezing parameter.

Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength $\chi$ of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator $\hat{J}_{x}$, we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of $(2\gamma)^{1/3}$ below super-Heisenberg limit $\propto 1/N^{3/2}$ for particle number $N$ and the dephasing rate $1<\!<\gamma

The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cramér-Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum quantum Fisher information with form N 2 for a given photon number distribution by a POVM in linear two-path interferometer phase measurement. We present a series of specified superposed states with infinite quantum Fisher information but with finite average photon numbers. The advantage of this unbounded quantum Fisher information will be beneficial to many applications in quantum technology.

Optimal measurement scheme with an efficient data processing is important in quantum-enhanced interferometry. Here we prove that for a general binary-outcome measurement, the simplest data processing based on inverting the average signal can saturate the Cramér-Rao bound. This idea is illustrated by binary-outcome homodyne detection, even-odd photon counting (i.e., parity detection), and zero-nonzero photon counting that have achieved super-resolved interferometric fringe and shot-noise limited sensitivity in coherent-light MachZehnder interferometer. The roles of phase diffusion are investigated in these binary-outcome measurements. We find that the diffusion degrades the fringe resolution and the achievable phase sensitivity. Our analytical results confirm that the zero-nonzero counting can produce a slightly better sensitivity than that of the parity detection, as demonstrated in a recent experiment.

The precise calculations of Wigner's d matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using Wigner's formula suffer from a loss of precision. We present a simple method to avoid this problem by expanding the d matrix into a complex Fourier series and calculate the Fourier coefficients by exactly diagonalizing the angular momentum operator J(y) in the eigenbasis of J(z). This method allows us to compute the d matrix and its various derivatives for spins up to a few thousand. The precision of the d matrix from our method is about 10(-14) for spins up to 100.