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Motional Gaussian states and gates for a levitating particle
Ondřej Černotík and Radim Filip
Department of Optics, Palacký University Olomouc,
17. listopadu 1192/12, 77146 Olomouc, Czechia
ondrej.cernotik@upol.cz
Squeezing in one dimension
Comparison to conventional optomechanics
Convetional optomechanics
relies on a dispersive shift of
the cavity resonance, using
tweezer only for trapping.
Conventional opto-
mechanics requires one
cavity per motional
mode for control. Full
control over the motion
needs also interactions
between mechanical
modes which are
difficult to engineer.
Coherent scattering
Optomechanical interaction is mediated by tweezer
photons scattered off the particle [1]. This coupling
enables control of all three centre-of-mass modes using
a single cavity mode [2,3].
Tunability of interactions
intracavity intensity
radial coupling
axial coupling
The coupling strength for axial and radial
modes is controlled by positioning the particle
within the cavity standing wave. The relative
strength for the two radial modes is set by the
polarization of the cavity and tweezer fields.
Highlights
Future plans
Multidimensional motion
Applications
creating genuine three-mode entanglement
novel states for quantum sensing below the standard
quantum limit and testing quantum mechanics
ultimate goal: full quantum control of particle motion
Nonlinear motion
higher-order optomechanical coupling [4]
nonlinear potential with non-Gaussian tweezers [5]
coupling to two-level systems [6]
cavity-mediated interactions
Radial and axial mode:
Two radial modes:
free oscillations and thermal noise cavity-mediated collective dissipation
The radial and axial modes couple to orthogonal field quadratures which has important implications for the effective interactions.
Interactions between mechanical modes can be induced by virtual photons (two radial modes), collective dissipation, or
measurement-based feedback. This is not straightforward with standard dispersive optomechanics.
References
[1] C. Gonzalez-Ballestero et al., PRA, 100, 013805 (2019).
[2] U. Delić et al., PRL 122, 123602 (2019).
[3] D. Windey et al., PRL 122, 123601 (2019).
[4] U. Delić et al., arXiv:1902.06605.
[5] M. Šiler et al., PRL, 121, 230601 (2018).
[6] G.P. Conangla et al., Nano Lett. 18, 3956 (2018).
10 2
10 1
100
Modulation depth
10 6
10 4
10 2
100
Squeezingdegree
100
101
SqueezedvarianceVsq
101
104
107
Thermal noise n
100
101
102
10 2
10 1
100
Sideband ratio / m
0.5
1.0
1.5
Basic Hamiltonian
Equations of motion
Adiabatic elimination of cavity dynamics
Assuming a large detuning between the tweezer and cavity
frequencies, , we get the effective mechanical dynamics
with the effecitve rates
10 3
10 2
10 1
100
Modulation depth
10 3
10 2
10 1
Effectiveparameters
|eff|/m,eff/m
0 250 500 750 1000
Time mt
10 6
10 3
100
Squeezingdegree
100
10 4
10 2
100
102
104
Initial temperature n0
10 1
100
101
102
SqueezedvarianceVsq
0 /2 3 /2 2
Modulation phase
10 1
100
Amplitude modulation of the tweezer
Modulation of the tweezer field results in parametric amplification of the motion and modulation of the optomechanical
coupling according to
with modulation depth and phase .
Adiabatic elimination of the cavity field now leads to the
effective mechanical dynamics
with
, leading to a lower instability
threshold and stronger squeezing.
When we choose the detuning ,
the cavity field couples to the Bogoliubov mode
via the Hamiltonian
where .
Combination of parametric and dissipative squeezing
leads to stronger squeezing than either technique
alone.
parametric
squeezing dissipative
squeezing
this approach opens the way towards full control of particle
motion via coherent scattering
strong mechanical squeezing possible with parametric
amplification and coherent scattering
prospect of interactions between all centre-of-mass modes
, stable
, unstable
state-of-the-art parameters [2]
state-of-the-art parameters [2]
dissipative squeezing alone
state-of-the-art parameters [2] (top)
and enhanced coupling (bottom)
0 5 10 15 20
0.90
0.95
1.00
Squeezingdegree
1.0
1.2
1.4
0 100 200 300 400 500
Time mt
10 6
10 3
100
100
101
10 3
100
103
Initial temperature n0
10 1
100
101
102
103
SqueezedvarianceVsq
state of the art
unstable
unstable
stable

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Motional Gaussian states and gates for a levitating particle

  • 1. Motional Gaussian states and gates for a levitating particle Ondřej Černotík and Radim Filip Department of Optics, Palacký University Olomouc, 17. listopadu 1192/12, 77146 Olomouc, Czechia ondrej.cernotik@upol.cz Squeezing in one dimension Comparison to conventional optomechanics Convetional optomechanics relies on a dispersive shift of the cavity resonance, using tweezer only for trapping. Conventional opto- mechanics requires one cavity per motional mode for control. Full control over the motion needs also interactions between mechanical modes which are difficult to engineer. Coherent scattering Optomechanical interaction is mediated by tweezer photons scattered off the particle [1]. This coupling enables control of all three centre-of-mass modes using a single cavity mode [2,3]. Tunability of interactions intracavity intensity radial coupling axial coupling The coupling strength for axial and radial modes is controlled by positioning the particle within the cavity standing wave. The relative strength for the two radial modes is set by the polarization of the cavity and tweezer fields. Highlights Future plans Multidimensional motion Applications creating genuine three-mode entanglement novel states for quantum sensing below the standard quantum limit and testing quantum mechanics ultimate goal: full quantum control of particle motion Nonlinear motion higher-order optomechanical coupling [4] nonlinear potential with non-Gaussian tweezers [5] coupling to two-level systems [6] cavity-mediated interactions Radial and axial mode: Two radial modes: free oscillations and thermal noise cavity-mediated collective dissipation The radial and axial modes couple to orthogonal field quadratures which has important implications for the effective interactions. Interactions between mechanical modes can be induced by virtual photons (two radial modes), collective dissipation, or measurement-based feedback. This is not straightforward with standard dispersive optomechanics. References [1] C. Gonzalez-Ballestero et al., PRA, 100, 013805 (2019). [2] U. Delić et al., PRL 122, 123602 (2019). [3] D. Windey et al., PRL 122, 123601 (2019). [4] U. Delić et al., arXiv:1902.06605. [5] M. Šiler et al., PRL, 121, 230601 (2018). [6] G.P. Conangla et al., Nano Lett. 18, 3956 (2018). 10 2 10 1 100 Modulation depth 10 6 10 4 10 2 100 Squeezingdegree 100 101 SqueezedvarianceVsq 101 104 107 Thermal noise n 100 101 102 10 2 10 1 100 Sideband ratio / m 0.5 1.0 1.5 Basic Hamiltonian Equations of motion Adiabatic elimination of cavity dynamics Assuming a large detuning between the tweezer and cavity frequencies, , we get the effective mechanical dynamics with the effecitve rates 10 3 10 2 10 1 100 Modulation depth 10 3 10 2 10 1 Effectiveparameters |eff|/m,eff/m 0 250 500 750 1000 Time mt 10 6 10 3 100 Squeezingdegree 100 10 4 10 2 100 102 104 Initial temperature n0 10 1 100 101 102 SqueezedvarianceVsq 0 /2 3 /2 2 Modulation phase 10 1 100 Amplitude modulation of the tweezer Modulation of the tweezer field results in parametric amplification of the motion and modulation of the optomechanical coupling according to with modulation depth and phase . Adiabatic elimination of the cavity field now leads to the effective mechanical dynamics with , leading to a lower instability threshold and stronger squeezing. When we choose the detuning , the cavity field couples to the Bogoliubov mode via the Hamiltonian where . Combination of parametric and dissipative squeezing leads to stronger squeezing than either technique alone. parametric squeezing dissipative squeezing this approach opens the way towards full control of particle motion via coherent scattering strong mechanical squeezing possible with parametric amplification and coherent scattering prospect of interactions between all centre-of-mass modes , stable , unstable state-of-the-art parameters [2] state-of-the-art parameters [2] dissipative squeezing alone state-of-the-art parameters [2] (top) and enhanced coupling (bottom) 0 5 10 15 20 0.90 0.95 1.00 Squeezingdegree 1.0 1.2 1.4 0 100 200 300 400 500 Time mt 10 6 10 3 100 100 101 10 3 100 103 Initial temperature n0 10 1 100 101 102 103 SqueezedvarianceVsq state of the art unstable unstable stable