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arXiv:0901.2824 · Physical Review A

Qubit coherent control and entanglement with squeezed light fields

Ephraim Shahmoon, Shimon Levit, Roee Ozeri

Published Sep 2, 2009• 6 citations
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Abstract

We study the use of squeezed light for qubit coherent control and compare it with the coherent-state control field case. We calculate the entanglement between a short pulse of resonant squeezed light and a two-level atom in free space and the resulting operation error. We find that the squeezing phase, the phase of the light field, and the atomic superposition phase all determine whether atom-pulse mode entanglement and the gate error are enhanced or suppressed. When averaged over all possible qubit initial states, the gate error would not decrease by a practically useful amount and would in fact increase in most cases. However, the enhanced entanglement may be of use in quantum communication schemes. We discuss the possibility of measuring the increased gate error as a signature of the enhancement of entanglement by squeezing.

DOI
10.1103/physreva.80.033803

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We study the use of squeezed light for qubit coherent control and compare it with the coherent-state control field case. We calculate the entanglement between a short pulse of resonant squeezed light and a two-level atom in free space and the resulting operation error. We find that the squeezing phase, the phase of the light field, and the atomic superposition phase all determine whether atom-pulse mode entanglement and the gate error are enhanced or suppressed. When averaged over all possible qubit initial states, the gate error would not decrease by a practically useful amount and would in fact increase in most cases. However, the enhanced entanglement may be of use in quantum communication schemes. We discuss the possibility of measuring the increased gate error as a signature of the enhancement of entanglement by squeezing.
In order to improve the error probability of generating entanglement by communication for quantum computation, we propose the use of squeezed light. When generating entanglement between two atoms by communication, the error probability can be reduced by increasing the distance between quantum states of probe light in phase space. The phase rotation of light depends on the atom-photon coupling strength and the light amplitude, which are limited in practice. A large error probability has been expected for coherent probe light. If we assume typical values of light amplitude and phase rotation, $\ensuremath{\alpha}=100$ and $\ensuremath{\theta}=0.01$, the error probability is estimated to be Pcoh(min)=0.14{P}_{\mathrm{coh}}^{(\mathrm{min})}=0.14Pcoh(min)​=0.14 and Pcoh(hom)=0.23{P}_{\mathrm{coh}}^{(\mathrm{hom})}=0.23Pcoh(hom)​=0.23 for minimum error discrimination and homodyne measurements. The error probability can be reduced to ${P}_{\mathrm{squ}}^{(\mathrm{min})}=1.73\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ and ${P}_{\mathrm{squ}}^{(\mathrm{hom})}=4.09\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ using squeezed coherent light, where the same values of the mean photon number and the phase rotation angle are assumed for the coherent light probe. These values satisfy the requirements for scalable quantum computation.
Quantum control of many body atomic spins is often pursued in the context of an atom-light quantum interface, where a quantized light field acts as a "quantum bus" that can be used to entangle distant atoms. One key challenge is to improve the coherence of the atom-light interface and the amount of atom-light entanglement it can generate, given the constraints of working with multilevel atoms and optical fields in a 3D geometry. We have explored new ways to achieve this, through rigorous optimization of the spatial geometry, and through control of the internal atomic state. Our basic setup consists of a quantized probe beam passing through an atom cloud held in a dipole trap, first generating spin-probe entanglement through the Faraday interaction, and then using backaction from a measurement of the probe polarization to squeeze the collective atomic spin. The relevant figure of merit is the metrologically useful spin squeezing determined by the enhancement in the resolution of rotations of the collective spin, relative to the commonly used spin coherent state. With an optimized free-space geometry, and by using a 2-color probe scheme to suppress tensor light shifts, we achieve 3(2) dB of metrologically useful spin squeezing. We can further increase atom-light coupling by implementing internal state control to prepare spin states with larger initial projection noise relative to the spin coherent state. Under the right conditions this increase in projection noise can lead to stronger measurement backaction and increased atom-atom entanglement. With further internal state control the increased atom-atom entanglement can then be mapped to a basis where it corresponds to improved squeezing of, e.g., the physical spin-angular momentum or the collective atomic clock pseudospin. In practice, controlling the collective spin of N ~ 10⁶ atoms in this fashion is an extraordinarily difficult challenge because errors in the control of individual atoms tend to be highly correlated. By employing precise internal state control, we have prepared and detected projection noise limited "cat" states (which have initial projection noise that is larger by a factor of 2f = 8 for Cs relative to the spin coherent state) and estimate that we can generate up to 6.0(5) dB of metrologically useful spin squeezing, demonstrating the advantage of using the internal atomic structure as a resource for ensemble control.
The light squeezing effects in the system of two identical two-level atoms in the Bell state interacting with the two-mode entangled coherent states field are investigated by means of Schrdinger equation solution and numerical calculations.The results show that light squeezing effects not only depends on the mean photon numbers and atomic initial state but also the degree of entanglement of the two-mode entangled coherent state optics field,whereas the coupling between two atoms does not affect the light squeezing effects.The light squeezing effects does not appear for a special kind of Bell state |β11〉,however there can appear the light squeezing effects under some conditions for the other three Bell states.
Considering two identical two-level atoms interacting with a single-mode thermal field through two-photon processes, this paper studies the atomic coherence control on the entanglement between two two-level atoms, and finds that the entanglement is greatly enhanced due to the initial atomic coherence. The results show that the entanglement can be manipulated by changing the initial parameters of the system, such as the superposition coefficients and the relative phases of the initial atomic coherent state and the mean photon number of the cavity field.
In this paper, we analyzed squeezing in the information entropy, quantum state fidelity, and qubit-qubit entanglement in a time-dependent system. The proposed model consists of two qubits that interact with a two-mode electromagnetic field under the dissipation effect. An analytical solution is calculated by considering the constants for the equations of motion. The effect of the general form of the time-dependent for qubit-field coupling and the dissipation term on the temporal behavior of the qubit-qubit entanglement, quantum state fidelity, entropy, and variance squeezing are examined. It is shown that the intervals of entanglement caused more squeezing for the case of considering the time-dependent parameters. Additionally, the entanglement between the qubits became more substantial for the case of time dependence. Fidelity and negativity rapidly reached the minimum values by increasing the effect of the dissipation parameter. Moreover, the amount of variance squeezing and the amplitude of the oscillations decreased considerably when the time dependence increased, but the fluctuations increased substantially. We show the relation between entropy and variance squeezing in the presence and absence of the dissipation parameter during the interaction period. This result enables new parameters to control the degree of entanglement and squeezing, especially in quantum communication.