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Coupling

Hyperfine 

Hyperfine(parent=None)

Bases: LevelCoupling

This node represent level coupling between hyperfine state.

Examples:

- To reach the node from the start node:

>>> node = bloqade.start.hyperfine
>>> type(node)
<class 'bloqade.builder.coupling.Hyperfine'>

- Hyperfine level coupling have two reachable field nodes:

    - detuning term (See also [`Detuning`][bloqade.builder.field.Detuning])
    - rabi term (See also [`Rabi`][bloqade.builder.field.Rabi])

>>> hyp_detune = bloqade.start.hyperfine.detuning
>>> hyp_rabi = bloqade.start.hyperfine.rabi
Source code in src/bloqade/builder/base.py 
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def __init__(
    self,
    parent: Optional["Builder"] = None,
) -> None:
    self.__parent__ = parent

LevelCoupling 

LevelCoupling(parent=None)

Bases: Builder

Source code in src/bloqade/builder/base.py 
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def __init__(
    self,
    parent: Optional["Builder"] = None,
) -> None:
    self.__parent__ = parent

detuning property 

detuning

Specify the Detuning Field of your program. You will be able to specify the spatial modulation afterwards.

Returns:

Type Description
Detuning

Detuning: A program node representing the detuning field.
Background and Context

In the Many-Body Rydberg Hamiltonian:

\[ \frac{\mathcal{H}(t)}{\hbar} = \sum_j \frac{\Omega_j(t)}{2} \left( e^{i \phi_j(t) } | g_j \rangle \langle r_j | + e^{-i \phi_j(t) } | r_j \rangle \langle g_j | \right) - \sum_j \Delta_j(t) \hat{n}_j + \sum_{j < k} V_{jk} \hat{n}_j \hat{n}_k. \]

The detuning is specified by the term \(\Delta_j(t)\) and specifies how off-resonant the laser being applied to the atoms is from the atomic energy transition, which is driven by the Rabi frequency \(\Omega_j(t)\).

The detuning is described by a field, which is the summation of one or more drives, with the drive being the sum of a waveform and spatial modulation:

\[ \sum_j \Delta_j(t) = \sum_j \sum_a C^{a}_{j} f_{a}(t) \]

Note that the spatial modulation \(C_{j}\) scales how much of the detuning waveform is experienced by the atom at site \(j\). You can specify the scaling that all atoms feel to be identical (global detuning) or you can specify different scaling for different atoms (local detuning).

Examples 

from bloqade import start

# specify geometry, in this case just one atom
geometry = start.add_position((0,0))
# specify your coupling (either `rydberg` or `hyperfine`)
coupling = geometry.rydberg
# Begin specifying your detuning
coupling.detuning
Alternatively you may start with building your Rabi field and then reach the ability to build your detuning like so:

from bloqade import start
geometry = start.add_position((0,0))
coupling = geometry.rydberg
rabi_field = coupling.rabi.amplitude.uniform.constant(duration = 1.0, value = 1.0)
detuning = rabi_field.detuning
Applications
Potential Pitfalls

Bloqade allows you to build a field for the Detuning in the form of:

\[ \sum_j \Delta_j(t) = \sum_j \sum_a C^{a}_{j} f_{a}(t) \]

Where your field can contain multiple drives.

In reality the hardware only supports the following configuration:

\[ \Delta_{i}(t) = \Delta_{1}(t) + c_{i} \Delta_{2}(t) \]
\[ c_i \in [0, 1] \]
\[ \Delta_{2}(t) \leq 0 \]

Where \(\Delta_{1}(t)\) is your global detuning (establishable via uniform) and \(\Delta_{2}(t)\) is your local detuning waveform with the spatial modulation \(c_{i}\) establishable via location or scale.

Next Possible Steps

You may continue building your program via:

rabi property 

rabi

Specify the complex-valued Rabi field of your program.

The Rabi field is composed of a real-valued Amplitude and Phase field.

  • Next possible steps to build your program are creating the RabiAmplitude field and RabiPhase field of the field:
    • ...rabi.amplitude: To create the Rabi amplitude field
    • ...rabi.phase: To create the Rabi phase field

Rydberg 

Rydberg(parent=None)

Bases: LevelCoupling

This node represent level coupling of rydberg state.

Examples:

- To reach the node from the start node:

>>> node = bloqade.start.rydberg
>>> type(node)
<class 'bloqade.builder.coupling.Rydberg'>

- Rydberg level coupling have two reachable field nodes:

    - detuning term (See also [`Detuning`][bloqade.builder.field.Detuning])
    - rabi term (See also [`Rabi`][bloqade.builder.field.Rabi])

>>> ryd_detune = bloqade.start.rydberg.detuning
>>> ryd_rabi = bloqade.start.rydberg.rabi
Source code in src/bloqade/builder/base.py 
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def __init__(
    self,
    parent: Optional["Builder"] = None,
) -> None:
    self.__parent__ = parent