diff --git a/qcsys/devices/ats.py b/qcsys/devices/ats.py
index a893565..893c27f 100644
--- a/qcsys/devices/ats.py
+++ b/qcsys/devices/ats.py
@@ -24,6 +24,7 @@ def common_ops(self):
         ops["a"] = jqt.destroy(N)
         ops["a_dag"] = jqt.create(N)
         ops["phi"] = self.phi_zpf()*(ops["a"] + ops["a_dag"])  
+        ops["n"] = 1j * self.n_zpf() * (ops["a_dag"] - ops["a"])
         return ops
 
     def phi_zpf(self):
diff --git a/tutorials/ats-coupler/0-resonator-ats-resonator.ipynb b/tutorials/ats-coupler/0-resonator-ats-resonator.ipynb
index 214137e..67d0de1 100644
--- a/tutorials/ats-coupler/0-resonator-ats-resonator.ipynb
+++ b/tutorials/ats-coupler/0-resonator-ats-resonator.ipynb
@@ -33,35 +33,73 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 4,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'g_ex': Array(-0.00212182+0.j, dtype=complex128),\n",
+       " 'ω_ATS': Array(6.02181564, dtype=float64),\n",
+       " 'ω_ResonatorA': Array(4.99584201, dtype=float64),\n",
+       " 'ω_ResonatorB': Array(7.00151547, dtype=float64)}"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "# system, ϕ0, metrics0, system0 = get_system_normal_rar({})\n",
-    "ϕ0, metrics0, system0 = get_metrics_linear_rar({})"
+    "ϕ0, metrics0, system0 = get_metrics_linear_rar({})\n",
+    "metrics0"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'g_ex': Array(-0.00212182+0.j, dtype=complex128),\n",
-       " 'ω_ATS': Array(6.02181564, dtype=float64),\n",
-       " 'ω_ResonatorA': Array(4.99584201, dtype=float64),\n",
-       " 'ω_ResonatorB': Array(7.00151547, dtype=float64)}"
+       "Array([ 0.00000000e+00, -3.55271368e-06,  3.55271368e-06, -3.55271368e-06,\n",
+       "       -1.06581410e-05,  2.13162821e-05], dtype=float64)"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "metrics0"
+    "metrics, system, ϕ0, metrics0, system0 = get_metrics_normal_rar({})#{\"ResonatorA_frequency\": 3})\n",
+    "metrics[\"K_a\"]*1e9"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Array([-2.14061657e-01, -2.14015472e-01, -2.14154028e-01, -2.11546336e-01,\n",
+       "       -4.03521234e+01,  1.18006174e+05], dtype=float64)"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "metrics, system, ϕ0, metrics0, system0 = get_metrics_normal_rar({\n",
+    "    \"ATS__dE_J\": 37.0 * 0.01\n",
+    "})\n",
+    "metrics[\"K_a\"]*1e9"
    ]
   }
  ],
diff --git a/tutorials/ats-coupler/rar_helpers.py b/tutorials/ats-coupler/rar_helpers.py
index 4f04fb1..07722d5 100644
--- a/tutorials/ats-coupler/rar_helpers.py
+++ b/tutorials/ats-coupler/rar_helpers.py
@@ -254,4 +254,29 @@ def get_system_normal_rar(params):
     system = qs.System.create(devices, couplings=couplings)
     system.params["phi_c"] = phi_c
     system.params["phi_c_alternative"] = phi_c_alternative
-    return system, ϕ0, metrics0, system0
\ No newline at end of file
+    return system, ϕ0, metrics0, system0
+
+@jit
+def get_metrics_normal_rar(params):
+    """set up devices"""
+    system, ϕ0, metrics0, system0 = get_system_normal_rar(params)
+    a_indx = 2
+    c_indx = 1
+    b_indx = 0
+
+    epsilon_p = params.get("ATS__drive_strength", DRIVE_STRENGTH)
+
+    resonator_a = system.devices[a_indx]
+    ats = system.devices[c_indx]
+    resonator_b = system.devices[b_indx]
+
+    Es, kets = system.calculate_eig()
+
+    n_ats = 0
+    K_a = (Es[2:, n_ats, 0] - Es[1:-1, n_ats, 0]) - (
+        Es[1:-1, n_ats, 0] - Es[0:-2, n_ats, 0]
+    )
+    metrics = {}
+    metrics["K_a"] = K_a
+
+    return metrics, system, ϕ0, metrics0, system0
\ No newline at end of file